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 -7/1 -20/3 -6/1 -16/3 -14/3 -22/5 -4/1 -26/7 -18/5 -7/2 -10/3 -42/13 -14/5 -12/5 -7/3 -2/1 -7/4 -14/9 -42/29 -7/5 -14/11 -7/6 0/1 1/1 7/6 14/11 7/5 42/29 3/2 14/9 7/4 2/1 28/13 7/3 112/47 12/5 56/23 5/2 28/11 8/3 14/5 3/1 42/13 56/17 10/3 84/25 7/2 196/55 18/5 112/31 11/3 26/7 56/15 4/1 13/3 22/5 84/19 9/2 14/3 24/5 5/1 16/3 11/2 28/5 6/1 19/3 32/5 13/2 20/3 7/1 8/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -7/1 -1/1 -20/3 -2/3 -13/2 -2/3 -1/2 -19/3 -2/3 -3/5 -6/1 -1/2 0/1 -11/2 -1/1 0/1 -16/3 -2/3 0/1 -5/1 -1/2 0/1 -14/3 0/1 -23/5 0/1 1/2 -32/7 0/1 2/1 -9/2 -1/1 0/1 -22/5 -1/2 -1/3 -13/3 -1/6 0/1 -4/1 0/1 -15/4 -1/4 0/1 -26/7 0/1 1/5 -11/3 0/1 1/1 -29/8 0/1 1/1 -47/13 2/3 1/1 -18/5 1/1 1/0 -25/7 -2/1 1/0 -7/2 0/1 -31/9 1/2 2/3 -55/16 0/1 1/1 -24/7 0/1 2/3 -17/5 2/3 1/1 -27/8 0/1 1/1 -10/3 1/1 1/0 -23/7 0/1 1/0 -36/11 0/1 -13/4 0/1 1/0 -42/13 1/1 -29/9 1/1 2/1 -16/5 0/1 2/1 -3/1 0/1 1/0 -14/5 1/0 -25/9 -4/1 1/0 -11/4 -3/1 -2/1 -30/11 -2/1 -5/3 -19/7 -4/3 -1/1 -46/17 -1/1 -1/2 -27/10 -1/1 0/1 -8/3 -2/1 0/1 -21/8 -1/1 -55/21 -1/1 0/1 -34/13 -1/1 -1/2 -13/5 0/1 1/2 -31/12 -2/1 1/0 -18/7 1/1 1/0 -5/2 -2/1 1/0 -27/11 -2/1 -1/1 -22/9 -3/2 -1/1 -17/7 -1/1 -2/3 -29/12 -1/1 0/1 -70/29 -1/1 -41/17 -3/4 -2/3 -12/5 0/1 -31/13 4/1 1/0 -50/21 -4/1 1/0 -19/8 -2/1 -1/1 -26/11 0/1 1/1 -7/3 1/0 -30/13 -2/1 -1/1 -83/36 -1/1 0/1 -53/23 -2/1 1/0 -23/10 -2/1 1/0 -16/7 -2/1 0/1 -25/11 0/1 1/0 -34/15 -3/1 1/0 -9/4 -2/1 -1/1 -29/13 -1/1 0/1 -20/9 0/1 -11/5 -2/1 -1/1 -24/11 -2/1 0/1 -13/6 0/1 1/0 -2/1 -1/1 1/0 -15/8 0/1 1/0 -28/15 1/0 -13/7 -2/1 1/0 -11/6 -1/1 0/1 -31/17 -2/1 1/0 -20/11 -2/1 -29/16 -2/1 -1/1 -9/5 -1/1 0/1 -25/14 -2/1 1/0 -16/9 -2/1 0/1 -23/13 0/1 1/0 -7/4 1/0 -33/19 -2/1 1/0 -59/34 -2/1 1/0 -26/15 -3/1 -2/1 -19/11 -1/1 0/1 -50/29 2/1 1/0 -81/47 10/1 1/0 -112/65 1/0 -31/18 -6/1 1/0 -43/25 -4/1 -7/2 -12/7 -2/1 -41/24 -4/3 -5/4 -70/41 -1/1 -29/17 -2/1 -1/1 -17/10 -4/3 -1/1 -56/33 -1/1 -39/23 -1/1 -6/7 -22/13 -1/1 -1/2 -27/16 -1/1 0/1 -32/19 -2/3 0/1 -5/3 0/1 1/0 -28/17 1/0 -23/14 -6/1 1/0 -18/11 -3/1 1/0 -31/19 0/1 1/0 -44/27 -4/1 -13/8 -5/2 -2/1 -34/21 -3/2 -1/1 -55/34 -2/1 -1/1 -76/47 -2/1 -21/13 -1/1 -29/18 -2/1 -1/1 -8/5 -2/1 0/1 -27/17 -2/1 -1/1 -19/12 -1/1 -2/3 -30/19 -1/3 0/1 -11/7 0/1 1/1 -14/9 1/0 -17/11 -4/1 -3/1 -20/13 -2/1 -23/15 -2/1 1/0 -3/2 -2/1 1/0 -16/11 -4/1 -2/1 -29/20 -4/1 -3/1 -42/29 -3/1 -13/9 -2/1 1/0 -36/25 -2/1 -59/41 -2/1 1/0 -23/16 -2/1 1/0 -56/39 1/0 -33/23 -4/1 1/0 -10/7 -3/1 1/0 -47/33 -16/5 -3/1 -84/59 -3/1 -37/26 -3/1 -14/5 -27/19 -3/1 -2/1 -17/12 -3/1 -8/3 -41/29 -5/2 -2/1 -24/17 -8/3 -2/1 -7/5 -2/1 -32/23 -2/1 0/1 -57/41 -2/1 -1/1 -196/141 -1/1 -139/100 -1/1 -2/3 -82/59 -1/1 0/1 -25/18 0/1 1/0 -18/13 -3/1 1/0 -65/47 -10/3 -3/1 -112/81 -3/1 -47/34 -3/1 -8/3 -29/21 -3/1 -2/1 -40/29 -8/3 -2/1 -11/8 -3/1 -2/1 -26/19 -11/5 -2/1 -41/30 -29/14 -2/1 -56/41 -2/1 -15/11 -2/1 -7/4 -4/3 -2/1 -13/10 -2/1 -11/6 -22/17 -5/3 -3/2 -53/41 -14/9 -3/2 -84/65 -3/2 -31/24 -3/2 -4/3 -9/7 -2/1 -1/1 -14/11 -2/1 -19/15 -2/1 -9/5 -43/34 -2/1 -7/4 -24/19 -2/1 -12/7 -29/23 -2/1 -5/3 -5/4 -2/1 -3/2 -16/13 -2/1 -4/3 -27/22 -2/1 -1/1 -11/9 -2/1 -1/1 -28/23 -2/1 -17/14 -2/1 -5/3 -6/5 -2/1 -3/2 -19/16 -7/5 -4/3 -32/27 -2/1 -4/3 -13/11 -3/2 -4/3 -20/17 -4/3 -27/23 -4/3 -1/1 -7/6 -1/1 -8/7 -2/1 -4/3 -1/1 -2/1 -1/1 0/1 -1/1 1/1 -1/1 -2/3 7/6 -1/1 20/17 -4/5 13/11 -4/5 -3/4 19/16 -4/5 -7/9 6/5 -3/4 -2/3 11/9 -1/1 -2/3 16/13 -4/5 -2/3 5/4 -3/4 -2/3 14/11 -2/3 23/18 -2/3 -5/8 32/25 -2/3 -4/7 9/7 -1/1 -2/3 22/17 -3/4 -5/7 13/10 -11/16 -2/3 4/3 -2/3 15/11 -7/10 -2/3 26/19 -2/3 -11/17 11/8 -2/3 -3/5 29/21 -2/3 -3/5 47/34 -8/13 -3/5 18/13 -3/5 -1/2 25/18 -1/2 0/1 7/5 -2/3 31/22 -5/8 -8/13 55/39 -2/3 -3/5 24/17 -2/3 -8/13 17/12 -8/13 -3/5 27/19 -2/3 -3/5 10/7 -3/5 -1/2 23/16 -2/3 -1/2 36/25 -2/3 13/9 -2/3 -1/2 42/29 -3/5 29/20 -3/5 -4/7 16/11 -2/3 -4/7 3/2 -2/3 -1/2 14/9 -1/2 25/16 -1/2 -2/5 11/7 -1/3 0/1 30/19 0/1 1/1 19/12 -2/1 -1/1 46/29 -1/1 -3/4 27/17 -1/1 -2/3 8/5 -2/3 0/1 21/13 -1/1 55/34 -1/1 -2/3 34/21 -1/1 -3/4 13/8 -2/3 -5/8 31/19 -1/2 0/1 18/11 -3/5 -1/2 5/3 -1/2 0/1 27/16 -1/1 0/1 22/13 -1/1 1/0 17/10 -1/1 -4/5 29/17 -1/1 -2/3 70/41 -1/1 41/24 -5/6 -4/5 12/7 -2/3 31/18 -6/11 -1/2 50/29 -1/2 -2/5 19/11 -1/1 0/1 26/15 -2/3 -3/5 7/4 -1/2 30/17 -1/1 0/1 83/47 -1/1 -2/3 53/30 -1/2 0/1 23/13 -1/2 0/1 16/9 -2/3 0/1 25/14 -2/3 -1/2 34/19 -1/2 -1/3 9/5 -1/1 0/1 29/16 -1/1 -2/3 20/11 -2/3 11/6 -1/1 0/1 24/13 -2/3 0/1 13/7 -2/3 -1/2 2/1 -1/1 -1/2 15/7 -2/3 -1/2 28/13 -1/2 13/6 -1/2 0/1 11/5 -1/1 -2/3 31/14 -1/2 0/1 20/9 0/1 29/13 -1/1 0/1 9/4 -1/1 -2/3 25/11 -1/2 0/1 16/7 -2/3 0/1 23/10 -2/3 -1/2 7/3 -1/2 33/14 -1/2 0/1 59/25 -1/2 0/1 26/11 -1/3 0/1 19/8 -1/1 -2/3 50/21 -4/7 -1/2 81/34 -12/23 -1/2 112/47 -1/2 31/13 -1/2 -4/9 43/18 -2/5 -3/8 12/5 0/1 41/17 -2/1 -3/2 70/29 -1/1 29/12 -1/1 0/1 17/7 -2/1 -1/1 56/23 -1/1 39/16 -1/1 -8/9 22/9 -1/1 -3/4 27/11 -1/1 -2/3 32/13 -4/5 -2/3 5/2 -2/3 -1/2 28/11 -1/2 23/9 -1/2 -4/9 18/7 -1/2 -1/3 31/12 -2/3 -1/2 44/17 -2/5 13/5 -1/4 0/1 34/13 -1/1 1/0 55/21 -1/1 0/1 76/29 0/1 21/8 -1/1 29/11 -1/1 0/1 8/3 -2/3 0/1 27/10 -1/1 0/1 19/7 -1/1 -4/5 30/11 -5/7 -2/3 11/4 -2/3 -3/5 14/5 -1/2 17/6 -2/5 -1/3 20/7 0/1 23/8 -1/2 0/1 3/1 -1/2 0/1 16/5 -2/5 0/1 29/9 -2/5 -1/3 42/13 -1/3 13/4 -1/2 0/1 36/11 0/1 59/18 -1/2 0/1 23/7 -1/2 0/1 56/17 -1/2 33/10 -1/2 -2/5 10/3 -1/2 -1/3 47/14 -6/17 -1/3 84/25 -1/3 37/11 -1/3 -4/13 27/8 -1/3 0/1 17/5 -1/3 -2/7 41/12 -1/4 0/1 24/7 -2/7 0/1 7/2 0/1 32/9 -2/3 0/1 57/16 -1/1 0/1 196/55 -1/1 139/39 -1/1 -4/5 82/23 -1/1 -2/3 25/7 -2/3 -1/2 18/5 -1/2 -1/3 65/18 -4/11 -1/3 112/31 -1/3 47/13 -1/3 -2/7 29/8 -1/3 0/1 40/11 -2/7 0/1 11/3 -1/3 0/1 26/7 -1/7 0/1 41/11 -1/16 0/1 56/15 0/1 15/4 0/1 1/2 4/1 0/1 13/3 0/1 1/4 22/5 1/1 1/0 53/12 4/1 1/0 84/19 1/0 31/7 -2/1 1/0 9/2 -1/1 0/1 14/3 0/1 19/4 0/1 1/3 43/9 0/1 1/2 24/5 0/1 2/3 29/6 0/1 1/1 5/1 0/1 1/0 16/3 -2/1 0/1 27/5 -1/1 0/1 11/2 -1/1 0/1 28/5 0/1 17/3 0/1 1/1 6/1 0/1 1/0 19/3 -3/1 -2/1 32/5 -2/1 0/1 13/2 -2/1 1/0 20/3 -2/1 27/4 -2/1 -1/1 7/1 -1/1 8/1 -2/1 0/1 1/0 -1/1 0/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(29,224,-18,-139) (-7/1,1/0) -> (-21/13,-29/18) Hyperbolic Matrix(139,952,-86,-589) (-7/1,-20/3) -> (-76/47,-21/13) Hyperbolic Matrix(111,728,34,223) (-20/3,-13/2) -> (13/4,36/11) Hyperbolic Matrix(167,1064,-132,-841) (-13/2,-19/3) -> (-19/15,-43/34) Hyperbolic Matrix(169,1064,98,617) (-19/3,-6/1) -> (50/29,19/11) Hyperbolic Matrix(29,168,-24,-139) (-6/1,-11/2) -> (-17/14,-6/5) Hyperbolic Matrix(113,616,-82,-447) (-11/2,-16/3) -> (-40/29,-11/8) Hyperbolic Matrix(85,448,48,253) (-16/3,-5/1) -> (23/13,16/9) Hyperbolic Matrix(83,392,-18,-85) (-5/1,-14/3) -> (-14/3,-23/5) Parabolic Matrix(195,896,-116,-533) (-23/5,-32/7) -> (-32/19,-5/3) Hyperbolic Matrix(197,896,-166,-755) (-32/7,-9/2) -> (-19/16,-32/27) 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(27,112,20,83) (-13/3,-4/1) -> (4/3,15/11) Hyperbolic Matrix(29,112,22,85) (-4/1,-15/4) -> (13/10,4/3) 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(169,616,-138,-503) (-11/3,-29/8) -> (-27/22,-11/9) Hyperbolic Matrix(449,1624,248,897) (-29/8,-47/13) -> (9/5,29/16) Hyperbolic Matrix(559,2016,-404,-1457) (-47/13,-18/5) -> (-18/13,-65/47) Hyperbolic Matrix(281,1008,172,617) (-18/5,-25/7) -> (31/19,18/11) Hyperbolic Matrix(111,392,-32,-113) (-25/7,-7/2) -> (-7/2,-31/9) Parabolic Matrix(1595,5488,-692,-2381) (-31/9,-55/16) -> (-83/36,-53/23) Hyperbolic Matrix(587,2016,122,419) (-55/16,-24/7) -> (24/5,29/6) Hyperbolic Matrix(197,672,-90,-307) (-24/7,-17/5) -> (-11/5,-24/11) Hyperbolic 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(169,560,-118,-391) (-10/3,-23/7) -> (-33/23,-10/7) Hyperbolic Matrix(393,1288,-256,-839) (-23/7,-36/11) -> (-20/13,-23/15) Hyperbolic Matrix(223,728,34,111) (-36/11,-13/4) -> (13/2,20/3) Hyperbolic Matrix(813,2632,476,1541) (-13/4,-42/13) -> (70/41,41/24) 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(141,448,62,197) (-16/5,-3/1) -> (25/11,16/7) Hyperbolic Matrix(139,392,-50,-141) (-3/1,-14/5) -> (-14/5,-25/9) Parabolic Matrix(223,616,-122,-337) (-25/9,-11/4) -> (-11/6,-31/17) Hyperbolic Matrix(225,616,164,449) (-11/4,-30/11) -> (26/19,11/8) Hyperbolic Matrix(391,1064,226,615) (-30/11,-19/7) -> (19/11,26/15) Hyperbolic Matrix(869,2352,-610,-1651) (-19/7,-46/17) -> (-10/7,-47/33) Hyperbolic Matrix(83,224,10,27) (-27/10,-8/3) -> (8/1,1/0) Hyperbolic Matrix(85,224,-74,-195) (-8/3,-21/8) -> (-7/6,-8/7) Hyperbolic Matrix(363,952,-310,-813) (-21/8,-55/21) -> (-27/23,-7/6) Hyperbolic Matrix(813,2128,332,869) (-55/21,-34/13) -> (22/9,27/11) 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(197,504,-120,-307) (-18/7,-5/2) -> (-23/14,-18/11) Hyperbolic Matrix(113,280,-90,-223) (-5/2,-27/11) -> (-29/23,-5/4) Hyperbolic Matrix(869,2128,332,813) (-27/11,-22/9) -> (34/13,55/21) Hyperbolic Matrix(505,1232,-298,-727) (-22/9,-17/7) -> (-39/23,-22/13) Hyperbolic Matrix(393,952,116,281) (-17/7,-29/12) -> (27/8,17/5) Hyperbolic Matrix(1345,3248,928,2241) (-29/12,-70/29) -> (42/29,29/20) Hyperbolic Matrix(1091,2632,754,1819) (-70/29,-41/17) -> (13/9,42/29) Hyperbolic Matrix(813,1960,314,757) (-41/17,-12/5) -> (44/17,13/5) Hyperbolic Matrix(727,1736,-446,-1065) (-12/5,-31/13) -> (-31/19,-44/27) Hyperbolic Matrix(2351,5600,-1364,-3249) (-31/13,-50/21) -> (-50/29,-81/47) Hyperbolic Matrix(447,1064,376,895) (-50/21,-19/8) -> (19/16,6/5) 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(559,1288,194,447) (-53/23,-23/10) -> (23/8,3/1) Hyperbolic Matrix(195,448,158,363) (-23/10,-16/7) -> (16/13,5/4) Hyperbolic Matrix(197,448,62,141) (-16/7,-25/11) -> (3/1,16/5) Hyperbolic Matrix(1037,2352,-802,-1819) (-25/11,-34/15) -> (-22/17,-53/41) Hyperbolic Matrix(727,1624,526,1175) (-9/4,-29/13) -> (29/21,47/34) Hyperbolic Matrix(503,1120,-428,-953) (-29/13,-20/9) -> (-20/17,-27/23) Hyperbolic Matrix(253,560,-164,-363) (-20/9,-11/5) -> (-17/11,-20/13) Hyperbolic Matrix(617,1344,-488,-1063) (-24/11,-13/6) -> (-43/34,-24/19) Hyperbolic Matrix(27,56,-14,-29) (-13/6,-2/1) -> (-2/1,-15/8) Parabolic Matrix(419,784,194,363) (-15/8,-28/15) -> (28/13,13/6) Hyperbolic Matrix(421,784,196,365) (-28/15,-13/7) -> (15/7,28/13) Hyperbolic Matrix(365,672,-258,-475) (-13/7,-11/6) -> (-17/12,-41/29) Hyperbolic Matrix(1261,2296,-876,-1595) (-31/17,-20/11) -> (-36/25,-59/41) Hyperbolic Matrix(1821,3304,-1126,-2043) (-20/11,-29/16) -> (-55/34,-76/47) Hyperbolic Matrix(897,1624,248,449) (-29/16,-9/5) -> (47/13,29/8) Hyperbolic Matrix(281,504,-218,-391) (-9/5,-25/14) -> (-31/24,-9/7) Hyperbolic Matrix(251,448,172,307) (-25/14,-16/9) -> (16/11,3/2) Hyperbolic Matrix(253,448,48,85) (-16/9,-23/13) -> (5/1,16/3) Hyperbolic Matrix(223,392,-128,-225) (-23/13,-7/4) -> (-7/4,-33/19) Parabolic Matrix(1903,3304,580,1007) (-33/19,-59/34) -> (59/18,23/7) Hyperbolic Matrix(3163,5488,-2276,-3949) (-59/34,-26/15) -> (-82/59,-25/18) Hyperbolic Matrix(615,1064,226,391) (-26/15,-19/11) -> (19/7,30/11) Hyperbolic Matrix(617,1064,98,169) (-19/11,-50/29) -> (6/1,19/3) Hyperbolic Matrix(7279,12544,3054,5263) (-81/47,-112/65) -> (112/47,31/13) Hyperbolic Matrix(7281,12544,3056,5265) (-112/65,-31/18) -> (81/34,112/47) Hyperbolic Matrix(587,1008,244,419) (-43/25,-12/7) -> (12/5,41/17) Hyperbolic Matrix(589,1008,246,421) (-12/7,-41/24) -> (43/18,12/5) Hyperbolic Matrix(1541,2632,476,813) (-41/24,-70/41) -> (42/13,13/4) 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(1847,3136,758,1287) (-17/10,-56/33) -> (56/23,39/16) Hyperbolic Matrix(1849,3136,760,1289) (-56/33,-39/23) -> (17/7,56/23) Hyperbolic Matrix(1259,2128,778,1315) (-22/13,-27/16) -> (55/34,34/21) Hyperbolic Matrix(1595,2688,448,755) (-27/16,-32/19) -> (32/9,57/16) Hyperbolic Matrix(475,784,186,307) (-5/3,-28/17) -> (28/11,23/9) Hyperbolic Matrix(477,784,188,309) (-28/17,-23/14) -> (5/2,28/11) Hyperbolic Matrix(617,1008,172,281) (-18/11,-31/19) -> (25/7,18/5) Hyperbolic Matrix(1203,1960,704,1147) (-44/27,-13/8) -> (41/24,12/7) Hyperbolic Matrix(449,728,346,561) (-13/8,-34/21) -> (22/17,13/10) Hyperbolic Matrix(1315,2128,778,1259) (-34/21,-55/34) -> (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(251,392,-162,-253) (-11/7,-14/9) -> (-14/9,-17/11) Parabolic Matrix(841,1288,476,729) (-23/15,-3/2) -> (53/30,23/13) Hyperbolic Matrix(307,448,172,251) (-3/2,-16/11) -> (16/9,25/14) Hyperbolic Matrix(1119,1624,308,447) (-16/11,-29/20) -> (29/8,40/11) Hyperbolic Matrix(2241,3248,928,1345) (-29/20,-42/29) -> (70/29,29/12) Hyperbolic Matrix(1819,2632,754,1091) (-42/29,-13/9) -> (41/17,70/29) 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(2183,3136,662,951) (-23/16,-56/39) -> (56/17,33/10) Hyperbolic Matrix(2185,3136,664,953) (-56/39,-33/23) -> (23/7,56/17) Hyperbolic Matrix(4955,7056,1474,2099) (-47/33,-84/59) -> (84/25,37/11) Hyperbolic Matrix(4957,7056,1476,2101) (-84/59,-37/26) -> (47/14,84/25) Hyperbolic Matrix(671,952,394,559) (-27/19,-17/12) -> (17/10,29/17) Hyperbolic Matrix(1149,1624,-970,-1371) (-41/29,-24/17) -> (-32/27,-13/11) Hyperbolic Matrix(279,392,-200,-281) (-24/17,-7/5) -> (-7/5,-32/23) Parabolic Matrix(1933,2688,786,1093) (-32/23,-57/41) -> (27/11,32/13) Hyperbolic Matrix(27635,38416,7754,10779) (-57/41,-196/141) -> (196/55,139/39) Hyperbolic Matrix(27637,38416,7756,10781) (-196/141,-139/100) -> (57/16,196/55) 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(449,616,164,225) (-11/8,-26/19) -> (30/11,11/4) 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(83,112,20,27) (-15/11,-4/3) -> (4/1,13/3) Hyperbolic Matrix(85,112,22,29) (-4/3,-13/10) -> (15/4,4/1) Hyperbolic Matrix(561,728,346,449) (-13/10,-22/17) -> (34/21,13/8) Hyperbolic Matrix(5459,7056,1234,1595) (-53/41,-84/65) -> (84/19,31/7) Hyperbolic Matrix(5461,7056,1236,1597) (-84/65,-31/24) -> (53/12,84/19) Hyperbolic Matrix(307,392,-242,-309) (-9/7,-14/11) -> (-14/11,-19/15) Parabolic Matrix(1597,2016,1132,1429) (-24/19,-29/23) -> (55/39,24/17) Hyperbolic Matrix(363,448,158,195) (-5/4,-16/13) -> (16/7,23/10) Hyperbolic Matrix(729,896,502,617) (-16/13,-27/22) -> (29/20,16/11) Hyperbolic Matrix(643,784,114,139) (-11/9,-28/23) -> (28/5,17/3) Hyperbolic Matrix(645,784,116,141) (-28/23,-17/14) -> (11/2,28/5) Hyperbolic Matrix(895,1064,376,447) (-6/5,-19/16) -> (19/8,50/21) Hyperbolic Matrix(617,728,428,505) (-13/11,-20/17) -> (36/25,13/9) Hyperbolic Matrix(197,224,124,141) (-8/7,-1/1) -> (27/17,8/5) Hyperbolic Matrix(1,0,2,1) (-1/1,0/1) -> (0/1,1/1) Parabolic Matrix(195,-224,74,-85) (1/1,7/6) -> (21/8,29/11) Hyperbolic Matrix(813,-952,310,-363) (7/6,20/17) -> (76/29,21/8) Hyperbolic Matrix(897,-1064,188,-223) (13/11,19/16) -> (19/4,43/9) Hyperbolic Matrix(139,-168,24,-29) (6/5,11/9) -> (17/3,6/1) Hyperbolic Matrix(503,-616,138,-169) (11/9,16/13) -> (40/11,11/3) Hyperbolic Matrix(309,-392,242,-307) (5/4,14/11) -> (14/11,23/18) Parabolic Matrix(701,-896,284,-363) (23/18,32/25) -> (32/13,5/2) Hyperbolic Matrix(699,-896,110,-141) (32/25,9/7) -> (19/3,32/5) Hyperbolic Matrix(391,-504,218,-281) (9/7,22/17) -> (34/19,9/5) Hyperbolic Matrix(1065,-1456,286,-391) (15/11,26/19) -> (26/7,41/11) 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(3893,-5488,2204,-3107) (31/22,55/39) -> (83/47,53/30) Hyperbolic Matrix(475,-672,258,-365) (24/17,17/12) -> (11/6,24/13) Hyperbolic Matrix(1063,-1512,670,-953) (27/19,10/7) -> (46/29,27/17) Hyperbolic Matrix(391,-560,118,-169) (10/7,23/16) -> (33/10,10/3) Hyperbolic Matrix(895,-1288,312,-449) (23/16,36/25) -> (20/7,23/8) Hyperbolic Matrix(253,-392,162,-251) (3/2,14/9) -> (14/9,25/16) Parabolic Matrix(393,-616,178,-279) (25/16,11/7) -> (11/5,31/14) Hyperbolic Matrix(1483,-2352,442,-701) (19/12,46/29) -> (10/3,47/14) Hyperbolic Matrix(139,-224,18,-29) (8/5,21/13) -> (7/1,8/1) Hyperbolic Matrix(589,-952,86,-139) (21/13,55/34) -> (27/4,7/1) Hyperbolic Matrix(1065,-1736,446,-727) (13/8,31/19) -> (31/13,43/18) Hyperbolic Matrix(307,-504,120,-197) (18/11,5/3) -> (23/9,18/7) Hyperbolic Matrix(167,-280,34,-57) (5/3,27/16) -> (29/6,5/1) Hyperbolic Matrix(727,-1232,298,-505) (22/13,17/10) -> (39/16,22/9) Hyperbolic Matrix(1009,-1736,390,-671) (12/7,31/18) -> (31/12,44/17) Hyperbolic Matrix(3249,-5600,1364,-2351) (31/18,50/29) -> (50/21,81/34) Hyperbolic Matrix(225,-392,128,-223) (26/15,7/4) -> (7/4,30/17) Parabolic Matrix(6217,-10976,1744,-3079) (30/17,83/47) -> (139/39,82/23) Hyperbolic Matrix(1315,-2352,298,-533) (25/14,34/19) -> (22/5,53/12) Hyperbolic Matrix(617,-1120,92,-167) (29/16,20/11) -> (20/3,27/4) Hyperbolic Matrix(307,-560,108,-197) (20/11,11/6) -> (17/6,20/7) Hyperbolic Matrix(727,-1344,152,-281) (24/13,13/7) -> (43/9,24/5) Hyperbolic Matrix(29,-56,14,-27) (13/7,2/1) -> (2/1,15/7) Parabolic Matrix(307,-672,90,-197) (13/6,11/5) -> (17/5,41/12) Hyperbolic Matrix(1035,-2296,316,-701) (31/14,20/9) -> (36/11,59/18) Hyperbolic Matrix(1483,-3304,566,-1261) (20/9,29/13) -> (55/21,76/29) Hyperbolic Matrix(223,-504,50,-113) (9/4,25/11) -> (31/7,9/2) Hyperbolic Matrix(169,-392,72,-167) (23/10,7/3) -> (7/3,33/14) Parabolic Matrix(2325,-5488,652,-1539) (59/25,26/11) -> (82/23,25/7) Hyperbolic Matrix(559,-1512,166,-449) (27/10,19/7) -> (37/11,27/8) Hyperbolic Matrix(141,-392,50,-139) (11/4,14/5) -> (14/5,17/6) Parabolic Matrix(475,-1624,74,-253) (41/12,24/7) -> (32/5,13/2) Hyperbolic Matrix(113,-392,32,-111) (24/7,7/2) -> (7/2,32/9) Parabolic Matrix(85,-392,18,-83) (9/2,14/3) -> (14/3,19/4) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(29,224,-18,-139) -> Matrix(3,2,-2,-1) Matrix(139,952,-86,-589) -> Matrix(5,4,-4,-3) Matrix(111,728,34,223) -> Matrix(3,2,-8,-5) Matrix(167,1064,-132,-841) -> Matrix(17,12,-10,-7) Matrix(169,1064,98,617) -> Matrix(3,2,-8,-5) Matrix(29,168,-24,-139) -> Matrix(7,2,-4,-1) Matrix(113,616,-82,-447) -> Matrix(1,-2,0,1) Matrix(85,448,48,253) -> Matrix(1,0,0,1) Matrix(83,392,-18,-85) -> Matrix(1,0,4,1) Matrix(195,896,-116,-533) -> Matrix(1,0,-2,1) Matrix(197,896,-166,-755) -> Matrix(3,-4,-2,3) Matrix(113,504,-50,-223) -> Matrix(3,2,-2,-1) Matrix(167,728,64,279) -> Matrix(1,0,2,1) Matrix(27,112,20,83) -> Matrix(5,2,-8,-3) Matrix(29,112,22,85) -> Matrix(3,-2,-4,3) Matrix(391,1456,-286,-1065) -> Matrix(21,-2,-10,1) Matrix(167,616,106,391) -> Matrix(1,0,-4,1) Matrix(169,616,-138,-503) -> Matrix(1,-2,0,1) Matrix(449,1624,248,897) -> Matrix(3,-2,-4,3) Matrix(559,2016,-404,-1457) -> Matrix(1,-4,0,1) Matrix(281,1008,172,617) -> Matrix(1,2,-2,-3) Matrix(111,392,-32,-113) -> Matrix(1,0,2,1) Matrix(1595,5488,-692,-2381) -> Matrix(1,0,-2,1) Matrix(587,2016,122,419) -> Matrix(1,0,0,1) Matrix(197,672,-90,-307) -> Matrix(1,0,-2,1) Matrix(281,952,116,393) -> Matrix(1,0,-2,1) Matrix(449,1512,-166,-559) -> Matrix(1,0,-2,1) Matrix(169,560,-118,-391) -> Matrix(1,-4,0,1) Matrix(393,1288,-256,-839) -> Matrix(1,-2,0,1) Matrix(223,728,34,111) -> Matrix(1,-2,0,1) Matrix(813,2632,476,1541) -> Matrix(5,-4,-6,5) Matrix(1007,3248,590,1903) -> Matrix(1,0,-2,1) Matrix(279,896,52,167) -> Matrix(1,-2,0,1) Matrix(141,448,62,197) -> Matrix(1,0,-2,1) Matrix(139,392,-50,-141) -> Matrix(1,-4,0,1) Matrix(223,616,-122,-337) -> Matrix(1,2,0,1) Matrix(225,616,164,449) -> Matrix(5,12,-8,-19) Matrix(391,1064,226,615) -> Matrix(3,4,-4,-5) Matrix(869,2352,-610,-1651) -> Matrix(7,4,-2,-1) Matrix(83,224,10,27) -> Matrix(1,0,0,1) Matrix(85,224,-74,-195) -> Matrix(3,2,-2,-1) Matrix(363,952,-310,-813) -> Matrix(5,4,-4,-3) Matrix(813,2128,332,869) -> Matrix(1,2,-2,-3) Matrix(279,728,64,167) -> Matrix(1,0,2,1) Matrix(671,1736,-390,-1009) -> Matrix(1,-4,0,1) Matrix(391,1008,282,727) -> Matrix(1,2,-2,-3) Matrix(197,504,-120,-307) -> Matrix(1,-4,0,1) Matrix(113,280,-90,-223) -> Matrix(3,8,-2,-5) Matrix(869,2128,332,813) -> Matrix(1,2,-2,-3) Matrix(505,1232,-298,-727) -> Matrix(3,4,-4,-5) Matrix(393,952,116,281) -> Matrix(1,0,-2,1) Matrix(1345,3248,928,2241) -> Matrix(1,4,-2,-7) Matrix(1091,2632,754,1819) -> Matrix(11,8,-18,-13) Matrix(813,1960,314,757) -> Matrix(3,2,-8,-5) Matrix(727,1736,-446,-1065) -> Matrix(1,-4,0,1) Matrix(2351,5600,-1364,-3249) -> Matrix(1,6,0,1) Matrix(447,1064,376,895) -> Matrix(3,10,-4,-13) Matrix(449,1064,284,673) -> Matrix(1,0,0,1) Matrix(167,392,-72,-169) -> Matrix(1,-2,0,1) Matrix(4759,10976,-3424,-7897) -> Matrix(1,2,-2,-3) Matrix(559,1288,194,447) -> Matrix(1,2,-2,-3) Matrix(195,448,158,363) -> Matrix(3,4,-4,-5) Matrix(197,448,62,141) -> Matrix(1,0,-2,1) Matrix(1037,2352,-802,-1819) -> Matrix(3,14,-2,-9) Matrix(727,1624,526,1175) -> Matrix(5,2,-8,-3) Matrix(503,1120,-428,-953) -> Matrix(5,4,-4,-3) Matrix(253,560,-164,-363) -> Matrix(1,-2,0,1) Matrix(617,1344,-488,-1063) -> Matrix(7,2,-4,-1) Matrix(27,56,-14,-29) -> Matrix(1,0,0,1) Matrix(419,784,194,363) -> Matrix(1,0,-2,1) Matrix(421,784,196,365) -> Matrix(1,4,-2,-7) Matrix(365,672,-258,-475) -> Matrix(5,8,-2,-3) Matrix(1261,2296,-876,-1595) -> Matrix(1,0,0,1) Matrix(1821,3304,-1126,-2043) -> Matrix(1,0,0,1) Matrix(897,1624,248,449) -> Matrix(1,2,-4,-7) Matrix(281,504,-218,-391) -> Matrix(3,2,-2,-1) Matrix(251,448,172,307) -> Matrix(1,4,-2,-7) Matrix(253,448,48,85) -> Matrix(1,0,0,1) Matrix(223,392,-128,-225) -> Matrix(1,-2,0,1) Matrix(1903,3304,580,1007) -> Matrix(1,2,-2,-3) Matrix(3163,5488,-2276,-3949) -> Matrix(1,2,0,1) Matrix(615,1064,226,391) -> Matrix(3,4,-4,-5) Matrix(617,1064,98,169) -> Matrix(1,-2,0,1) Matrix(7279,12544,3054,5263) -> Matrix(1,-14,-2,29) Matrix(7281,12544,3056,5265) -> Matrix(1,18,-2,-35) Matrix(587,1008,244,419) -> Matrix(1,2,0,1) Matrix(589,1008,246,421) -> Matrix(1,2,-4,-7) Matrix(1541,2632,476,813) -> Matrix(3,4,-10,-13) Matrix(1903,3248,590,1007) -> Matrix(1,0,-2,1) Matrix(559,952,394,671) -> Matrix(1,4,-2,-7) Matrix(1847,3136,758,1287) -> Matrix(11,12,-12,-13) Matrix(1849,3136,760,1289) -> Matrix(9,8,-8,-7) Matrix(1259,2128,778,1315) -> Matrix(1,2,-2,-3) Matrix(1595,2688,448,755) -> Matrix(1,0,0,1) Matrix(475,784,186,307) -> Matrix(1,-4,-2,9) Matrix(477,784,188,309) -> Matrix(1,8,-2,-15) Matrix(617,1008,172,281) -> Matrix(1,2,-2,-3) Matrix(1203,1960,704,1147) -> Matrix(3,10,-4,-13) Matrix(449,728,346,561) -> Matrix(7,12,-10,-17) Matrix(1315,2128,778,1259) -> Matrix(1,2,-2,-3) Matrix(279,448,104,167) -> Matrix(1,2,-2,-3) Matrix(281,448,106,169) -> Matrix(1,2,-2,-3) Matrix(953,1512,-670,-1063) -> Matrix(5,8,-2,-3) Matrix(673,1064,284,449) -> Matrix(1,0,0,1) Matrix(391,616,106,167) -> Matrix(1,0,-4,1) Matrix(251,392,-162,-253) -> Matrix(1,-4,0,1) Matrix(841,1288,476,729) -> Matrix(1,2,-2,-3) Matrix(307,448,172,251) -> Matrix(1,4,-2,-7) Matrix(1119,1624,308,447) -> Matrix(1,4,-4,-15) Matrix(2241,3248,928,1345) -> Matrix(1,4,-2,-7) Matrix(1819,2632,754,1091) -> Matrix(3,8,-2,-5) Matrix(505,728,428,617) -> Matrix(3,10,-4,-13) Matrix(2297,3304,974,1401) -> Matrix(1,2,-2,-3) Matrix(2183,3136,662,951) -> Matrix(1,0,-2,1) Matrix(2185,3136,664,953) -> Matrix(1,4,-2,-7) Matrix(4955,7056,1474,2099) -> Matrix(9,28,-28,-87) Matrix(4957,7056,1476,2101) -> Matrix(11,32,-32,-93) Matrix(671,952,394,559) -> Matrix(1,4,-2,-7) Matrix(1149,1624,-970,-1371) -> Matrix(5,14,-4,-11) Matrix(279,392,-200,-281) -> Matrix(3,8,-2,-5) Matrix(1933,2688,786,1093) -> Matrix(3,4,-4,-5) Matrix(27635,38416,7754,10779) -> Matrix(5,6,-6,-7) Matrix(27637,38416,7756,10781) -> Matrix(3,2,-2,-1) Matrix(727,1008,282,391) -> Matrix(1,2,-2,-3) Matrix(9071,12544,2510,3471) -> Matrix(5,16,-16,-51) Matrix(9073,12544,2512,3473) -> Matrix(7,20,-20,-57) Matrix(1175,1624,526,727) -> Matrix(1,2,0,1) Matrix(1177,1624,366,505) -> Matrix(3,8,-8,-21) Matrix(449,616,164,225) -> Matrix(5,12,-8,-19) Matrix(2295,3136,614,839) -> Matrix(1,2,16,33) Matrix(2297,3136,616,841) -> Matrix(1,2,-20,-39) Matrix(83,112,20,27) -> Matrix(1,2,0,1) Matrix(85,112,22,29) -> Matrix(1,2,-4,-7) Matrix(561,728,346,449) -> Matrix(7,12,-10,-17) Matrix(5459,7056,1234,1595) -> Matrix(13,20,-2,-3) Matrix(5461,7056,1236,1597) -> Matrix(11,16,2,3) Matrix(307,392,-242,-309) -> Matrix(7,16,-4,-9) Matrix(1597,2016,1132,1429) -> Matrix(3,4,-4,-5) Matrix(363,448,158,195) -> Matrix(3,4,-4,-5) Matrix(729,896,502,617) -> Matrix(7,10,-12,-17) Matrix(643,784,114,139) -> Matrix(1,2,0,1) Matrix(645,784,116,141) -> Matrix(1,2,-4,-7) Matrix(895,1064,376,447) -> Matrix(7,10,-12,-17) Matrix(617,728,428,505) -> Matrix(7,10,-12,-17) Matrix(197,224,124,141) -> Matrix(3,4,-4,-5) Matrix(1,0,2,1) -> Matrix(3,4,-4,-5) Matrix(195,-224,74,-85) -> Matrix(3,2,-2,-1) Matrix(813,-952,310,-363) -> Matrix(5,4,-4,-3) Matrix(897,-1064,188,-223) -> Matrix(5,4,6,5) Matrix(139,-168,24,-29) -> Matrix(3,2,4,3) Matrix(503,-616,138,-169) -> Matrix(3,2,-8,-5) Matrix(309,-392,242,-307) -> Matrix(23,16,-36,-25) Matrix(701,-896,284,-363) -> Matrix(13,8,-18,-11) Matrix(699,-896,110,-141) -> Matrix(7,4,-2,-1) Matrix(391,-504,218,-281) -> Matrix(3,2,-2,-1) Matrix(1065,-1456,286,-391) -> Matrix(3,2,-38,-25) Matrix(447,-616,82,-113) -> Matrix(3,2,-8,-5) Matrix(1457,-2016,404,-559) -> Matrix(7,4,-16,-9) Matrix(281,-392,200,-279) -> Matrix(11,8,-18,-13) Matrix(3893,-5488,2204,-3107) -> Matrix(13,8,-18,-11) Matrix(475,-672,258,-365) -> Matrix(13,8,-18,-11) Matrix(1063,-1512,670,-953) -> Matrix(13,8,-18,-11) Matrix(391,-560,118,-169) -> Matrix(7,4,-16,-9) Matrix(895,-1288,312,-449) -> Matrix(3,2,-8,-5) Matrix(253,-392,162,-251) -> Matrix(7,4,-16,-9) Matrix(393,-616,178,-279) -> Matrix(5,2,-8,-3) Matrix(1483,-2352,442,-701) -> Matrix(5,4,-14,-11) Matrix(139,-224,18,-29) -> Matrix(3,2,-2,-1) Matrix(589,-952,86,-139) -> Matrix(5,4,-4,-3) Matrix(1065,-1736,446,-727) -> Matrix(7,4,-16,-9) Matrix(307,-504,120,-197) -> Matrix(7,4,-16,-9) Matrix(167,-280,34,-57) -> Matrix(1,0,2,1) Matrix(727,-1232,298,-505) -> Matrix(3,4,-4,-5) Matrix(1009,-1736,390,-671) -> Matrix(7,4,-16,-9) Matrix(3249,-5600,1364,-2351) -> Matrix(13,6,-24,-11) Matrix(225,-392,128,-223) -> Matrix(3,2,-8,-5) Matrix(6217,-10976,1744,-3079) -> Matrix(1,2,-2,-3) Matrix(1315,-2352,298,-533) -> Matrix(5,2,2,1) Matrix(617,-1120,92,-167) -> Matrix(5,4,-4,-3) Matrix(307,-560,108,-197) -> Matrix(3,2,-8,-5) Matrix(727,-1344,152,-281) -> Matrix(3,2,4,3) Matrix(29,-56,14,-27) -> Matrix(1,0,0,1) Matrix(307,-672,90,-197) -> Matrix(1,0,-2,1) Matrix(1035,-2296,316,-701) -> Matrix(1,0,0,1) Matrix(1483,-3304,566,-1261) -> Matrix(1,0,0,1) Matrix(223,-504,50,-113) -> Matrix(3,2,-2,-1) Matrix(169,-392,72,-167) -> Matrix(3,2,-8,-5) Matrix(2325,-5488,652,-1539) -> Matrix(5,2,-8,-3) Matrix(559,-1512,166,-449) -> Matrix(1,0,-2,1) Matrix(141,-392,50,-139) -> Matrix(7,4,-16,-9) Matrix(475,-1624,74,-253) -> Matrix(7,2,-4,-1) Matrix(113,-392,32,-111) -> Matrix(1,0,2,1) Matrix(85,-392,18,-83) -> Matrix(1,0,4,1) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 6 Minimal number of generators: 2 Number of equivalence classes of cusps: 3 Genus: 0 Degree of H/liftables -> H/(image of liftables): 44 Degree of the the map X: 44 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 0/1 7/6 14/11 4/3 7/5 42/29 14/9 12/7 7/4 2/1 28/13 20/9 7/3 112/47 12/5 56/23 28/11 8/3 14/5 3/1 16/5 42/13 56/17 10/3 84/25 7/2 196/55 18/5 112/31 26/7 56/15 4/1 22/5 84/19 9/2 14/3 24/5 5/1 16/3 11/2 28/5 6/1 32/5 13/2 20/3 7/1 8/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES 0/1 -1/1 1/1 -1/1 -2/3 7/6 -1/1 20/17 -4/5 13/11 -4/5 -3/4 19/16 -4/5 -7/9 6/5 -3/4 -2/3 11/9 -1/1 -2/3 16/13 -4/5 -2/3 5/4 -3/4 -2/3 14/11 -2/3 23/18 -2/3 -5/8 32/25 -2/3 -4/7 9/7 -1/1 -2/3 22/17 -3/4 -5/7 13/10 -11/16 -2/3 4/3 -2/3 15/11 -7/10 -2/3 26/19 -2/3 -11/17 11/8 -2/3 -3/5 29/21 -2/3 -3/5 47/34 -8/13 -3/5 18/13 -3/5 -1/2 25/18 -1/2 0/1 7/5 -2/3 31/22 -5/8 -8/13 55/39 -2/3 -3/5 24/17 -2/3 -8/13 17/12 -8/13 -3/5 27/19 -2/3 -3/5 10/7 -3/5 -1/2 23/16 -2/3 -1/2 36/25 -2/3 13/9 -2/3 -1/2 42/29 -3/5 29/20 -3/5 -4/7 16/11 -2/3 -4/7 3/2 -2/3 -1/2 14/9 -1/2 25/16 -1/2 -2/5 11/7 -1/3 0/1 30/19 0/1 1/1 19/12 -2/1 -1/1 46/29 -1/1 -3/4 27/17 -1/1 -2/3 8/5 -2/3 0/1 21/13 -1/1 55/34 -1/1 -2/3 34/21 -1/1 -3/4 13/8 -2/3 -5/8 31/19 -1/2 0/1 18/11 -3/5 -1/2 5/3 -1/2 0/1 27/16 -1/1 0/1 22/13 -1/1 1/0 17/10 -1/1 -4/5 29/17 -1/1 -2/3 70/41 -1/1 41/24 -5/6 -4/5 12/7 -2/3 31/18 -6/11 -1/2 50/29 -1/2 -2/5 19/11 -1/1 0/1 26/15 -2/3 -3/5 7/4 -1/2 30/17 -1/1 0/1 83/47 -1/1 -2/3 53/30 -1/2 0/1 23/13 -1/2 0/1 16/9 -2/3 0/1 25/14 -2/3 -1/2 34/19 -1/2 -1/3 9/5 -1/1 0/1 29/16 -1/1 -2/3 20/11 -2/3 11/6 -1/1 0/1 24/13 -2/3 0/1 13/7 -2/3 -1/2 2/1 -1/1 -1/2 15/7 -2/3 -1/2 28/13 -1/2 13/6 -1/2 0/1 11/5 -1/1 -2/3 31/14 -1/2 0/1 20/9 0/1 29/13 -1/1 0/1 9/4 -1/1 -2/3 25/11 -1/2 0/1 16/7 -2/3 0/1 23/10 -2/3 -1/2 7/3 -1/2 33/14 -1/2 0/1 59/25 -1/2 0/1 26/11 -1/3 0/1 19/8 -1/1 -2/3 50/21 -4/7 -1/2 81/34 -12/23 -1/2 112/47 -1/2 31/13 -1/2 -4/9 43/18 -2/5 -3/8 12/5 0/1 41/17 -2/1 -3/2 70/29 -1/1 29/12 -1/1 0/1 17/7 -2/1 -1/1 56/23 -1/1 39/16 -1/1 -8/9 22/9 -1/1 -3/4 27/11 -1/1 -2/3 32/13 -4/5 -2/3 5/2 -2/3 -1/2 28/11 -1/2 23/9 -1/2 -4/9 18/7 -1/2 -1/3 31/12 -2/3 -1/2 44/17 -2/5 13/5 -1/4 0/1 34/13 -1/1 1/0 55/21 -1/1 0/1 76/29 0/1 21/8 -1/1 29/11 -1/1 0/1 8/3 -2/3 0/1 27/10 -1/1 0/1 19/7 -1/1 -4/5 30/11 -5/7 -2/3 11/4 -2/3 -3/5 14/5 -1/2 17/6 -2/5 -1/3 20/7 0/1 23/8 -1/2 0/1 3/1 -1/2 0/1 16/5 -2/5 0/1 29/9 -2/5 -1/3 42/13 -1/3 13/4 -1/2 0/1 36/11 0/1 59/18 -1/2 0/1 23/7 -1/2 0/1 56/17 -1/2 33/10 -1/2 -2/5 10/3 -1/2 -1/3 47/14 -6/17 -1/3 84/25 -1/3 37/11 -1/3 -4/13 27/8 -1/3 0/1 17/5 -1/3 -2/7 41/12 -1/4 0/1 24/7 -2/7 0/1 7/2 0/1 32/9 -2/3 0/1 57/16 -1/1 0/1 196/55 -1/1 139/39 -1/1 -4/5 82/23 -1/1 -2/3 25/7 -2/3 -1/2 18/5 -1/2 -1/3 65/18 -4/11 -1/3 112/31 -1/3 47/13 -1/3 -2/7 29/8 -1/3 0/1 40/11 -2/7 0/1 11/3 -1/3 0/1 26/7 -1/7 0/1 41/11 -1/16 0/1 56/15 0/1 15/4 0/1 1/2 4/1 0/1 13/3 0/1 1/4 22/5 1/1 1/0 53/12 4/1 1/0 84/19 1/0 31/7 -2/1 1/0 9/2 -1/1 0/1 14/3 0/1 19/4 0/1 1/3 43/9 0/1 1/2 24/5 0/1 2/3 29/6 0/1 1/1 5/1 0/1 1/0 16/3 -2/1 0/1 27/5 -1/1 0/1 11/2 -1/1 0/1 28/5 0/1 17/3 0/1 1/1 6/1 0/1 1/0 19/3 -3/1 -2/1 32/5 -2/1 0/1 13/2 -2/1 1/0 20/3 -2/1 27/4 -2/1 -1/1 7/1 -1/1 8/1 -2/1 0/1 1/0 -1/1 0/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,0,1,1) (0/1,1/0) -> (0/1,1/1) Parabolic Matrix(195,-224,74,-85) (1/1,7/6) -> (21/8,29/11) Hyperbolic Matrix(813,-952,310,-363) (7/6,20/17) -> (76/29,21/8) Hyperbolic Matrix(617,-728,189,-223) (20/17,13/11) -> (13/4,36/11) Hyperbolic Matrix(897,-1064,188,-223) (13/11,19/16) -> (19/4,43/9) Hyperbolic Matrix(895,-1064,519,-617) (19/16,6/5) -> (50/29,19/11) Hyperbolic Matrix(139,-168,24,-29) (6/5,11/9) -> (17/3,6/1) Hyperbolic Matrix(503,-616,138,-169) (11/9,16/13) -> (40/11,11/3) Hyperbolic Matrix(363,-448,205,-253) (16/13,5/4) -> (23/13,16/9) Hyperbolic Matrix(309,-392,242,-307) (5/4,14/11) -> (14/11,23/18) Parabolic Matrix(701,-896,284,-363) (23/18,32/25) -> (32/13,5/2) Hyperbolic Matrix(699,-896,110,-141) (32/25,9/7) -> (19/3,32/5) Hyperbolic Matrix(391,-504,218,-281) (9/7,22/17) -> (34/19,9/5) Hyperbolic Matrix(561,-728,215,-279) (22/17,13/10) -> (13/5,34/13) Hyperbolic Matrix(85,-112,63,-83) (13/10,4/3) -> (4/3,15/11) Parabolic Matrix(1065,-1456,286,-391) (15/11,26/19) -> (26/7,41/11) Hyperbolic Matrix(449,-616,285,-391) (26/19,11/8) -> (11/7,30/19) Hyperbolic Matrix(447,-616,82,-113) (11/8,29/21) -> (27/5,11/2) Hyperbolic Matrix(1175,-1624,649,-897) (29/21,47/34) -> (9/5,29/16) Hyperbolic Matrix(1457,-2016,404,-559) (47/34,18/13) -> (18/5,65/18) Hyperbolic Matrix(727,-1008,445,-617) (18/13,25/18) -> (31/19,18/11) Hyperbolic Matrix(281,-392,200,-279) (25/18,7/5) -> (7/5,31/22) Parabolic Matrix(3893,-5488,2204,-3107) (31/22,55/39) -> (83/47,53/30) Hyperbolic Matrix(1429,-2016,297,-419) (55/39,24/17) -> (24/5,29/6) Hyperbolic Matrix(475,-672,258,-365) (24/17,17/12) -> (11/6,24/13) Hyperbolic Matrix(671,-952,277,-393) (17/12,27/19) -> (29/12,17/7) Hyperbolic Matrix(1063,-1512,670,-953) (27/19,10/7) -> (46/29,27/17) Hyperbolic Matrix(391,-560,118,-169) (10/7,23/16) -> (33/10,10/3) Hyperbolic Matrix(895,-1288,312,-449) (23/16,36/25) -> (20/7,23/8) Hyperbolic Matrix(505,-728,77,-111) (36/25,13/9) -> (13/2,20/3) Hyperbolic Matrix(1819,-2632,1065,-1541) (13/9,42/29) -> (70/41,41/24) Hyperbolic Matrix(2241,-3248,1313,-1903) (42/29,29/20) -> (29/17,70/41) Hyperbolic Matrix(617,-896,115,-167) (29/20,16/11) -> (16/3,27/5) Hyperbolic Matrix(307,-448,135,-197) (16/11,3/2) -> (25/11,16/7) Hyperbolic Matrix(253,-392,162,-251) (3/2,14/9) -> (14/9,25/16) Parabolic Matrix(393,-616,178,-279) (25/16,11/7) -> (11/5,31/14) Hyperbolic Matrix(673,-1064,389,-615) (30/19,19/12) -> (19/11,26/15) Hyperbolic Matrix(1483,-2352,442,-701) (19/12,46/29) -> (10/3,47/14) Hyperbolic Matrix(141,-224,17,-27) (27/17,8/5) -> (8/1,1/0) Hyperbolic Matrix(139,-224,18,-29) (8/5,21/13) -> (7/1,8/1) Hyperbolic Matrix(589,-952,86,-139) (21/13,55/34) -> (27/4,7/1) Hyperbolic Matrix(1315,-2128,537,-869) (55/34,34/21) -> (22/9,27/11) Hyperbolic Matrix(449,-728,103,-167) (34/21,13/8) -> (13/3,22/5) Hyperbolic Matrix(1065,-1736,446,-727) (13/8,31/19) -> (31/13,43/18) Hyperbolic Matrix(307,-504,120,-197) (18/11,5/3) -> (23/9,18/7) Hyperbolic Matrix(167,-280,34,-57) (5/3,27/16) -> (29/6,5/1) Hyperbolic Matrix(1259,-2128,481,-813) (27/16,22/13) -> (34/13,55/21) Hyperbolic Matrix(727,-1232,298,-505) (22/13,17/10) -> (39/16,22/9) Hyperbolic Matrix(559,-952,165,-281) (17/10,29/17) -> (27/8,17/5) Hyperbolic Matrix(1147,-1960,443,-757) (41/24,12/7) -> (44/17,13/5) Hyperbolic Matrix(1009,-1736,390,-671) (12/7,31/18) -> (31/12,44/17) Hyperbolic Matrix(3249,-5600,1364,-2351) (31/18,50/29) -> (50/21,81/34) Hyperbolic Matrix(225,-392,128,-223) (26/15,7/4) -> (7/4,30/17) Parabolic Matrix(6217,-10976,1744,-3079) (30/17,83/47) -> (139/39,82/23) Hyperbolic Matrix(729,-1288,253,-447) (53/30,23/13) -> (23/8,3/1) Hyperbolic Matrix(251,-448,79,-141) (16/9,25/14) -> (3/1,16/5) Hyperbolic Matrix(1315,-2352,298,-533) (25/14,34/19) -> (22/5,53/12) Hyperbolic Matrix(617,-1120,92,-167) (29/16,20/11) -> (20/3,27/4) Hyperbolic Matrix(307,-560,108,-197) (20/11,11/6) -> (17/6,20/7) Hyperbolic Matrix(727,-1344,152,-281) (24/13,13/7) -> (43/9,24/5) Hyperbolic Matrix(29,-56,14,-27) (13/7,2/1) -> (2/1,15/7) Parabolic Matrix(365,-784,169,-363) (15/7,28/13) -> (28/13,13/6) Parabolic Matrix(307,-672,90,-197) (13/6,11/5) -> (17/5,41/12) Hyperbolic Matrix(1035,-2296,316,-701) (31/14,20/9) -> (36/11,59/18) Hyperbolic Matrix(1483,-3304,566,-1261) (20/9,29/13) -> (55/21,76/29) Hyperbolic Matrix(727,-1624,201,-449) (29/13,9/4) -> (47/13,29/8) Hyperbolic Matrix(223,-504,50,-113) (9/4,25/11) -> (31/7,9/2) Hyperbolic Matrix(195,-448,37,-85) (16/7,23/10) -> (5/1,16/3) Hyperbolic Matrix(169,-392,72,-167) (23/10,7/3) -> (7/3,33/14) Parabolic Matrix(1401,-3304,427,-1007) (33/14,59/25) -> (59/18,23/7) Hyperbolic Matrix(2325,-5488,652,-1539) (59/25,26/11) -> (82/23,25/7) Hyperbolic Matrix(449,-1064,165,-391) (26/11,19/8) -> (19/7,30/11) Hyperbolic Matrix(447,-1064,71,-169) (19/8,50/21) -> (6/1,19/3) Hyperbolic Matrix(5265,-12544,2209,-5263) (81/34,112/47) -> (112/47,31/13) Parabolic Matrix(421,-1008,175,-419) (43/18,12/5) -> (12/5,41/17) Parabolic Matrix(1091,-2632,337,-813) (41/17,70/29) -> (42/13,13/4) Hyperbolic Matrix(1345,-3248,417,-1007) (70/29,29/12) -> (29/9,42/13) Hyperbolic Matrix(1289,-3136,529,-1287) (17/7,56/23) -> (56/23,39/16) Parabolic Matrix(1093,-2688,307,-755) (27/11,32/13) -> (32/9,57/16) Hyperbolic Matrix(309,-784,121,-307) (5/2,28/11) -> (28/11,23/9) Parabolic Matrix(391,-1008,109,-281) (18/7,31/12) -> (25/7,18/5) Hyperbolic Matrix(169,-448,63,-167) (29/11,8/3) -> (8/3,27/10) Parabolic Matrix(559,-1512,166,-449) (27/10,19/7) -> (37/11,27/8) Hyperbolic Matrix(225,-616,61,-167) (30/11,11/4) -> (11/3,26/7) Hyperbolic Matrix(141,-392,50,-139) (11/4,14/5) -> (14/5,17/6) Parabolic Matrix(505,-1624,139,-447) (16/5,29/9) -> (29/8,40/11) Hyperbolic Matrix(953,-3136,289,-951) (23/7,56/17) -> (56/17,33/10) Parabolic Matrix(2101,-7056,625,-2099) (47/14,84/25) -> (84/25,37/11) Parabolic Matrix(475,-1624,74,-253) (41/12,24/7) -> (32/5,13/2) Hyperbolic Matrix(113,-392,32,-111) (24/7,7/2) -> (7/2,32/9) Parabolic Matrix(10781,-38416,3025,-10779) (57/16,196/55) -> (196/55,139/39) Parabolic Matrix(3473,-12544,961,-3471) (65/18,112/31) -> (112/31,47/13) Parabolic Matrix(841,-3136,225,-839) (41/11,56/15) -> (56/15,15/4) Parabolic Matrix(29,-112,7,-27) (15/4,4/1) -> (4/1,13/3) Parabolic Matrix(1597,-7056,361,-1595) (53/12,84/19) -> (84/19,31/7) Parabolic Matrix(85,-392,18,-83) (9/2,14/3) -> (14/3,19/4) Parabolic Matrix(141,-784,25,-139) (11/2,28/5) -> (28/5,17/3) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,0,1,1) -> Matrix(1,2,-2,-3) Matrix(195,-224,74,-85) -> Matrix(3,2,-2,-1) Matrix(813,-952,310,-363) -> Matrix(5,4,-4,-3) Matrix(617,-728,189,-223) -> Matrix(5,4,-14,-11) Matrix(897,-1064,188,-223) -> Matrix(5,4,6,5) Matrix(895,-1064,519,-617) -> Matrix(5,4,-14,-11) Matrix(139,-168,24,-29) -> Matrix(3,2,4,3) Matrix(503,-616,138,-169) -> Matrix(3,2,-8,-5) Matrix(363,-448,205,-253) -> Matrix(3,2,-2,-1) Matrix(309,-392,242,-307) -> Matrix(23,16,-36,-25) Matrix(701,-896,284,-363) -> Matrix(13,8,-18,-11) Matrix(699,-896,110,-141) -> Matrix(7,4,-2,-1) Matrix(391,-504,218,-281) -> Matrix(3,2,-2,-1) Matrix(561,-728,215,-279) -> Matrix(3,2,4,3) Matrix(85,-112,63,-83) -> Matrix(11,8,-18,-13) Matrix(1065,-1456,286,-391) -> Matrix(3,2,-38,-25) Matrix(449,-616,285,-391) -> Matrix(3,2,-14,-9) Matrix(447,-616,82,-113) -> Matrix(3,2,-8,-5) Matrix(1175,-1624,649,-897) -> Matrix(13,8,-18,-11) Matrix(1457,-2016,404,-559) -> Matrix(7,4,-16,-9) Matrix(727,-1008,445,-617) -> Matrix(1,0,0,1) Matrix(281,-392,200,-279) -> Matrix(11,8,-18,-13) Matrix(3893,-5488,2204,-3107) -> Matrix(13,8,-18,-11) Matrix(1429,-2016,297,-419) -> Matrix(3,2,-2,-1) Matrix(475,-672,258,-365) -> Matrix(13,8,-18,-11) Matrix(671,-952,277,-393) -> Matrix(3,2,-8,-5) Matrix(1063,-1512,670,-953) -> Matrix(13,8,-18,-11) Matrix(391,-560,118,-169) -> Matrix(7,4,-16,-9) Matrix(895,-1288,312,-449) -> Matrix(3,2,-8,-5) Matrix(505,-728,77,-111) -> Matrix(7,4,-2,-1) Matrix(1819,-2632,1065,-1541) -> Matrix(23,14,-28,-17) Matrix(2241,-3248,1313,-1903) -> Matrix(3,2,-8,-5) Matrix(617,-896,115,-167) -> Matrix(7,4,-2,-1) Matrix(307,-448,135,-197) -> Matrix(3,2,-8,-5) Matrix(253,-392,162,-251) -> Matrix(7,4,-16,-9) Matrix(393,-616,178,-279) -> Matrix(5,2,-8,-3) Matrix(673,-1064,389,-615) -> Matrix(1,2,-2,-3) Matrix(1483,-2352,442,-701) -> Matrix(5,4,-14,-11) Matrix(141,-224,17,-27) -> Matrix(3,2,-2,-1) Matrix(139,-224,18,-29) -> Matrix(3,2,-2,-1) Matrix(589,-952,86,-139) -> Matrix(5,4,-4,-3) Matrix(1315,-2128,537,-869) -> Matrix(1,0,0,1) Matrix(449,-728,103,-167) -> Matrix(3,2,4,3) Matrix(1065,-1736,446,-727) -> Matrix(7,4,-16,-9) Matrix(307,-504,120,-197) -> Matrix(7,4,-16,-9) Matrix(167,-280,34,-57) -> Matrix(1,0,2,1) Matrix(1259,-2128,481,-813) -> Matrix(1,0,0,1) Matrix(727,-1232,298,-505) -> Matrix(3,4,-4,-5) Matrix(559,-952,165,-281) -> Matrix(3,2,-8,-5) Matrix(1147,-1960,443,-757) -> Matrix(5,4,-14,-11) Matrix(1009,-1736,390,-671) -> Matrix(7,4,-16,-9) Matrix(3249,-5600,1364,-2351) -> Matrix(13,6,-24,-11) Matrix(225,-392,128,-223) -> Matrix(3,2,-8,-5) Matrix(6217,-10976,1744,-3079) -> Matrix(1,2,-2,-3) Matrix(729,-1288,253,-447) -> Matrix(1,0,0,1) Matrix(251,-448,79,-141) -> Matrix(3,2,-8,-5) Matrix(1315,-2352,298,-533) -> Matrix(5,2,2,1) Matrix(617,-1120,92,-167) -> Matrix(5,4,-4,-3) Matrix(307,-560,108,-197) -> Matrix(3,2,-8,-5) Matrix(727,-1344,152,-281) -> Matrix(3,2,4,3) Matrix(29,-56,14,-27) -> Matrix(1,0,0,1) Matrix(365,-784,169,-363) -> Matrix(3,2,-8,-5) Matrix(307,-672,90,-197) -> Matrix(1,0,-2,1) Matrix(1035,-2296,316,-701) -> Matrix(1,0,0,1) Matrix(1483,-3304,566,-1261) -> Matrix(1,0,0,1) Matrix(727,-1624,201,-449) -> Matrix(1,0,-2,1) Matrix(223,-504,50,-113) -> Matrix(3,2,-2,-1) Matrix(195,-448,37,-85) -> Matrix(3,2,-2,-1) Matrix(169,-392,72,-167) -> Matrix(3,2,-8,-5) Matrix(1401,-3304,427,-1007) -> Matrix(1,0,0,1) Matrix(2325,-5488,652,-1539) -> Matrix(5,2,-8,-3) Matrix(449,-1064,165,-391) -> Matrix(1,2,-2,-3) Matrix(447,-1064,71,-169) -> Matrix(7,4,-2,-1) Matrix(5265,-12544,2209,-5263) -> Matrix(31,16,-64,-33) Matrix(421,-1008,175,-419) -> Matrix(1,0,2,1) Matrix(1091,-2632,337,-813) -> Matrix(1,2,-4,-7) Matrix(1345,-3248,417,-1007) -> Matrix(3,2,-8,-5) Matrix(1289,-3136,529,-1287) -> Matrix(9,10,-10,-11) Matrix(1093,-2688,307,-755) -> Matrix(3,2,-2,-1) Matrix(309,-784,121,-307) -> Matrix(11,6,-24,-13) Matrix(391,-1008,109,-281) -> Matrix(1,0,0,1) Matrix(169,-448,63,-167) -> Matrix(1,0,0,1) Matrix(559,-1512,166,-449) -> Matrix(1,0,-2,1) Matrix(225,-616,61,-167) -> Matrix(3,2,-14,-9) Matrix(141,-392,50,-139) -> Matrix(7,4,-16,-9) Matrix(505,-1624,139,-447) -> Matrix(5,2,-18,-7) Matrix(953,-3136,289,-951) -> Matrix(3,2,-8,-5) Matrix(2101,-7056,625,-2099) -> Matrix(29,10,-90,-31) Matrix(475,-1624,74,-253) -> Matrix(7,2,-4,-1) Matrix(113,-392,32,-111) -> Matrix(1,0,2,1) Matrix(10781,-38416,3025,-10779) -> Matrix(3,4,-4,-5) Matrix(3473,-12544,961,-3471) -> Matrix(17,6,-54,-19) Matrix(841,-3136,225,-839) -> Matrix(1,0,18,1) Matrix(29,-112,7,-27) -> Matrix(1,0,2,1) Matrix(1597,-7056,361,-1595) -> Matrix(1,-6,0,1) Matrix(85,-392,18,-83) -> Matrix(1,0,4,1) Matrix(141,-784,25,-139) -> Matrix(1,0,2,1) 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 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): 22 ----------------------------------------------------------------------- INFORMATION ON THE IMAGE IN PGL(2,Z) OF THE GROUP OF EXTENDED MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE c d 0/1 -1/1 2 1 2/1 (-1/1,-1/2) 0 14 28/13 -1/2 2 1 13/6 (-1/2,0/1) 0 28 11/5 (-1/1,-2/3) 0 28 20/9 0/1 2 7 29/13 (-1/1,0/1) 0 28 9/4 (-1/1,-2/3) 0 28 25/11 (-1/2,0/1) 0 28 16/7 0 7 23/10 (-2/3,-1/2) 0 28 7/3 -1/2 1 4 33/14 (-1/2,0/1) 0 28 59/25 (-1/2,0/1) 0 28 26/11 (-1/3,0/1) 0 14 19/8 (-1/1,-2/3) 0 28 50/21 (-4/7,-1/2) 0 14 112/47 -1/2 16 1 31/13 (-1/2,-4/9) 0 28 12/5 0/1 2 7 41/17 (-2/1,-3/2) 0 28 70/29 -1/1 4 2 29/12 (-1/1,0/1) 0 28 17/7 (-2/1,-1/1) 0 28 56/23 -1/1 10 1 22/9 (-1/1,-3/4) 0 14 27/11 (-1/1,-2/3) 0 28 5/2 (-2/3,-1/2) 0 28 28/11 -1/2 6 1 18/7 (-1/2,-1/3) 0 14 31/12 (-2/3,-1/2) 0 28 44/17 -2/5 2 7 13/5 (-1/4,0/1) 0 28 34/13 (-1/1,1/0) 0 14 55/21 (-1/1,0/1) 0 28 21/8 -1/1 1 4 8/3 0 7 27/10 (-1/1,0/1) 0 28 19/7 (-1/1,-4/5) 0 28 30/11 (-5/7,-2/3) 0 14 11/4 (-2/3,-3/5) 0 28 14/5 -1/2 4 2 17/6 (-2/5,-1/3) 0 28 20/7 0/1 2 7 3/1 (-1/2,0/1) 0 28 16/5 0 7 29/9 (-2/5,-1/3) 0 28 42/13 -1/3 4 2 13/4 (-1/2,0/1) 0 28 36/11 0/1 2 7 59/18 (-1/2,0/1) 0 28 23/7 (-1/2,0/1) 0 28 56/17 -1/2 2 1 10/3 (-1/2,-1/3) 0 14 84/25 -1/3 10 1 37/11 (-1/3,-4/13) 0 28 27/8 (-1/3,0/1) 0 28 17/5 (-1/3,-2/7) 0 28 41/12 (-1/4,0/1) 0 28 24/7 0 7 7/2 0/1 1 4 32/9 0 7 57/16 (-1/1,0/1) 0 28 196/55 -1/1 4 1 82/23 (-1/1,-2/3) 0 14 25/7 (-2/3,-1/2) 0 28 18/5 (-1/2,-1/3) 0 14 112/31 -1/3 6 1 47/13 (-1/3,-2/7) 0 28 29/8 (-1/3,0/1) 0 28 11/3 (-1/3,0/1) 0 28 26/7 (-1/7,0/1) 0 14 56/15 0/1 18 1 15/4 (0/1,1/2) 0 28 4/1 0/1 2 7 13/3 (0/1,1/4) 0 28 22/5 (1/1,1/0) 0 14 84/19 1/0 6 1 31/7 (-2/1,1/0) 0 28 9/2 (-1/1,0/1) 0 28 14/3 0/1 4 2 19/4 (0/1,1/3) 0 28 24/5 0 7 29/6 (0/1,1/1) 0 28 5/1 (0/1,1/0) 0 28 16/3 0 7 27/5 (-1/1,0/1) 0 28 11/2 (-1/1,0/1) 0 28 28/5 0/1 2 1 6/1 (0/1,1/0) 0 14 19/3 (-3/1,-2/1) 0 28 32/5 0 7 13/2 (-2/1,1/0) 0 28 20/3 -2/1 2 7 27/4 (-2/1,-1/1) 0 28 7/1 -1/1 1 4 8/1 0 7 1/0 (-1/1,0/1) 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(1,0,1,-1) (0/1,2/1) -> (0/1,2/1) Reflection Matrix(27,-56,13,-27) (2/1,28/13) -> (2/1,28/13) Reflection Matrix(337,-728,156,-337) (28/13,13/6) -> (28/13,13/6) Reflection Matrix(307,-672,90,-197) (13/6,11/5) -> (17/5,41/12) Hyperbolic Matrix(253,-560,89,-197) (11/5,20/9) -> (17/6,20/7) Glide Reflection Matrix(503,-1120,75,-167) (20/9,29/13) -> (20/3,27/4) Glide Reflection Matrix(727,-1624,201,-449) (29/13,9/4) -> (47/13,29/8) Hyperbolic Matrix(223,-504,50,-113) (9/4,25/11) -> (31/7,9/2) Hyperbolic Matrix(197,-448,62,-141) (25/11,16/7) -> (3/1,16/5) Glide Reflection Matrix(195,-448,37,-85) (16/7,23/10) -> (5/1,16/3) Hyperbolic Matrix(169,-392,72,-167) (23/10,7/3) -> (7/3,33/14) Parabolic Matrix(1401,-3304,427,-1007) (33/14,59/25) -> (59/18,23/7) Hyperbolic Matrix(2325,-5488,652,-1539) (59/25,26/11) -> (82/23,25/7) Hyperbolic Matrix(449,-1064,165,-391) (26/11,19/8) -> (19/7,30/11) Hyperbolic Matrix(447,-1064,71,-169) (19/8,50/21) -> (6/1,19/3) Hyperbolic Matrix(2351,-5600,987,-2351) (50/21,112/47) -> (50/21,112/47) Reflection Matrix(2913,-6944,1222,-2913) (112/47,31/13) -> (112/47,31/13) Reflection Matrix(727,-1736,281,-671) (31/13,12/5) -> (31/12,44/17) Glide Reflection Matrix(813,-1960,314,-757) (12/5,41/17) -> (44/17,13/5) Glide Reflection Matrix(1091,-2632,337,-813) (41/17,70/29) -> (42/13,13/4) Hyperbolic Matrix(1345,-3248,417,-1007) (70/29,29/12) -> (29/9,42/13) Hyperbolic Matrix(393,-952,116,-281) (29/12,17/7) -> (27/8,17/5) Glide Reflection Matrix(783,-1904,322,-783) (17/7,56/23) -> (17/7,56/23) Reflection Matrix(505,-1232,207,-505) (56/23,22/9) -> (56/23,22/9) Reflection Matrix(869,-2128,332,-813) (22/9,27/11) -> (34/13,55/21) Glide Reflection Matrix(113,-280,23,-57) (27/11,5/2) -> (29/6,5/1) Glide Reflection Matrix(111,-280,44,-111) (5/2,28/11) -> (5/2,28/11) Reflection Matrix(197,-504,77,-197) (28/11,18/7) -> (28/11,18/7) Reflection Matrix(391,-1008,109,-281) (18/7,31/12) -> (25/7,18/5) Hyperbolic Matrix(279,-728,64,-167) (13/5,34/13) -> (13/3,22/5) Glide Reflection Matrix(363,-952,53,-139) (55/21,21/8) -> (27/4,7/1) Glide Reflection Matrix(85,-224,11,-29) (21/8,8/3) -> (7/1,8/1) Glide Reflection Matrix(83,-224,10,-27) (8/3,27/10) -> (8/1,1/0) Glide Reflection Matrix(559,-1512,166,-449) (27/10,19/7) -> (37/11,27/8) Hyperbolic Matrix(225,-616,61,-167) (30/11,11/4) -> (11/3,26/7) Hyperbolic Matrix(141,-392,50,-139) (11/4,14/5) -> (14/5,17/6) Parabolic Matrix(449,-1288,137,-393) (20/7,3/1) -> (36/11,59/18) Glide Reflection Matrix(279,-896,52,-167) (16/5,29/9) -> (16/3,27/5) Glide Reflection Matrix(223,-728,34,-111) (13/4,36/11) -> (13/2,20/3) Glide Reflection Matrix(783,-2576,238,-783) (23/7,56/17) -> (23/7,56/17) Reflection Matrix(169,-560,51,-169) (56/17,10/3) -> (56/17,10/3) Reflection Matrix(251,-840,75,-251) (10/3,84/25) -> (10/3,84/25) Reflection Matrix(1849,-6216,550,-1849) (84/25,37/11) -> (84/25,37/11) Reflection Matrix(475,-1624,74,-253) (41/12,24/7) -> (32/5,13/2) Hyperbolic Matrix(113,-392,32,-111) (24/7,7/2) -> (7/2,32/9) Parabolic Matrix(645,-2296,134,-477) (32/9,57/16) -> (24/5,29/6) Glide Reflection Matrix(6271,-22344,1760,-6271) (57/16,196/55) -> (57/16,196/55) Reflection Matrix(4509,-16072,1265,-4509) (196/55,82/23) -> (196/55,82/23) Reflection Matrix(559,-2016,155,-559) (18/5,112/31) -> (18/5,112/31) Reflection Matrix(2913,-10528,806,-2913) (112/31,47/13) -> (112/31,47/13) Reflection Matrix(169,-616,31,-113) (29/8,11/3) -> (27/5,11/2) Glide Reflection Matrix(391,-1456,105,-391) (26/7,56/15) -> (26/7,56/15) Reflection Matrix(449,-1680,120,-449) (56/15,15/4) -> (56/15,15/4) Reflection Matrix(29,-112,7,-27) (15/4,4/1) -> (4/1,13/3) Parabolic Matrix(419,-1848,95,-419) (22/5,84/19) -> (22/5,84/19) Reflection Matrix(1177,-5208,266,-1177) (84/19,31/7) -> (84/19,31/7) Reflection Matrix(85,-392,18,-83) (9/2,14/3) -> (14/3,19/4) Parabolic Matrix(223,-1064,35,-167) (19/4,24/5) -> (19/3,32/5) Glide Reflection Matrix(111,-616,20,-111) (11/2,28/5) -> (11/2,28/5) Reflection Matrix(29,-168,5,-29) (28/5,6/1) -> (28/5,6/1) Reflection IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,0,0,-1) -> Matrix(-1,0,2,1) (0/1,1/0) -> (-1/1,0/1) Matrix(1,0,1,-1) -> Matrix(3,2,-4,-3) (0/1,2/1) -> (-1/1,-1/2) Matrix(27,-56,13,-27) -> Matrix(3,2,-4,-3) (2/1,28/13) -> (-1/1,-1/2) Matrix(337,-728,156,-337) -> Matrix(-1,0,4,1) (28/13,13/6) -> (-1/2,0/1) Matrix(307,-672,90,-197) -> Matrix(1,0,-2,1) 0/1 Matrix(253,-560,89,-197) -> Matrix(-1,0,4,1) *** -> (-1/2,0/1) Matrix(503,-1120,75,-167) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(727,-1624,201,-449) -> Matrix(1,0,-2,1) 0/1 Matrix(223,-504,50,-113) -> Matrix(3,2,-2,-1) -1/1 Matrix(197,-448,62,-141) -> Matrix(-1,0,4,1) *** -> (-1/2,0/1) Matrix(195,-448,37,-85) -> Matrix(3,2,-2,-1) -1/1 Matrix(169,-392,72,-167) -> Matrix(3,2,-8,-5) -1/2 Matrix(1401,-3304,427,-1007) -> Matrix(1,0,0,1) Matrix(2325,-5488,652,-1539) -> Matrix(5,2,-8,-3) -1/2 Matrix(449,-1064,165,-391) -> Matrix(1,2,-2,-3) -1/1 Matrix(447,-1064,71,-169) -> Matrix(7,4,-2,-1) Matrix(2351,-5600,987,-2351) -> Matrix(15,8,-28,-15) (50/21,112/47) -> (-4/7,-1/2) Matrix(2913,-6944,1222,-2913) -> Matrix(17,8,-36,-17) (112/47,31/13) -> (-1/2,-4/9) Matrix(727,-1736,281,-671) -> Matrix(5,2,-12,-5) *** -> (-1/2,-1/3) Matrix(813,-1960,314,-757) -> Matrix(1,2,-2,-5) Matrix(1091,-2632,337,-813) -> Matrix(1,2,-4,-7) Matrix(1345,-3248,417,-1007) -> Matrix(3,2,-8,-5) -1/2 Matrix(393,-952,116,-281) -> Matrix(-1,0,4,1) *** -> (-1/2,0/1) Matrix(783,-1904,322,-783) -> Matrix(3,4,-2,-3) (17/7,56/23) -> (-2/1,-1/1) Matrix(505,-1232,207,-505) -> Matrix(7,6,-8,-7) (56/23,22/9) -> (-1/1,-3/4) Matrix(869,-2128,332,-813) -> Matrix(3,2,-4,-3) *** -> (-1/1,-1/2) Matrix(113,-280,23,-57) -> Matrix(3,2,2,1) Matrix(111,-280,44,-111) -> Matrix(7,4,-12,-7) (5/2,28/11) -> (-2/3,-1/2) Matrix(197,-504,77,-197) -> Matrix(5,2,-12,-5) (28/11,18/7) -> (-1/2,-1/3) Matrix(391,-1008,109,-281) -> Matrix(1,0,0,1) Matrix(279,-728,64,-167) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(363,-952,53,-139) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(85,-224,11,-29) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(83,-224,10,-27) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(559,-1512,166,-449) -> Matrix(1,0,-2,1) 0/1 Matrix(225,-616,61,-167) -> Matrix(3,2,-14,-9) Matrix(141,-392,50,-139) -> Matrix(7,4,-16,-9) -1/2 Matrix(449,-1288,137,-393) -> Matrix(-1,0,4,1) *** -> (-1/2,0/1) Matrix(279,-896,52,-167) -> Matrix(5,2,-2,-1) Matrix(223,-728,34,-111) -> Matrix(5,2,-2,-1) Matrix(783,-2576,238,-783) -> Matrix(-1,0,4,1) (23/7,56/17) -> (-1/2,0/1) Matrix(169,-560,51,-169) -> Matrix(5,2,-12,-5) (56/17,10/3) -> (-1/2,-1/3) Matrix(251,-840,75,-251) -> Matrix(5,2,-12,-5) (10/3,84/25) -> (-1/2,-1/3) Matrix(1849,-6216,550,-1849) -> Matrix(25,8,-78,-25) (84/25,37/11) -> (-1/3,-4/13) Matrix(475,-1624,74,-253) -> Matrix(7,2,-4,-1) Matrix(113,-392,32,-111) -> Matrix(1,0,2,1) 0/1 Matrix(645,-2296,134,-477) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(6271,-22344,1760,-6271) -> Matrix(-1,0,2,1) (57/16,196/55) -> (-1/1,0/1) Matrix(4509,-16072,1265,-4509) -> Matrix(5,4,-6,-5) (196/55,82/23) -> (-1/1,-2/3) Matrix(559,-2016,155,-559) -> Matrix(5,2,-12,-5) (18/5,112/31) -> (-1/2,-1/3) Matrix(2913,-10528,806,-2913) -> Matrix(13,4,-42,-13) (112/31,47/13) -> (-1/3,-2/7) Matrix(169,-616,31,-113) -> Matrix(-1,0,4,1) *** -> (-1/2,0/1) Matrix(391,-1456,105,-391) -> Matrix(-1,0,14,1) (26/7,56/15) -> (-1/7,0/1) Matrix(449,-1680,120,-449) -> Matrix(1,0,4,-1) (56/15,15/4) -> (0/1,1/2) Matrix(29,-112,7,-27) -> Matrix(1,0,2,1) 0/1 Matrix(419,-1848,95,-419) -> Matrix(-1,2,0,1) (22/5,84/19) -> (1/1,1/0) Matrix(1177,-5208,266,-1177) -> Matrix(1,4,0,-1) (84/19,31/7) -> (-2/1,1/0) Matrix(85,-392,18,-83) -> Matrix(1,0,4,1) 0/1 Matrix(223,-1064,35,-167) -> Matrix(3,-2,-2,1) Matrix(111,-616,20,-111) -> Matrix(-1,0,2,1) (11/2,28/5) -> (-1/1,0/1) Matrix(29,-168,5,-29) -> Matrix(1,0,0,-1) (28/5,6/1) -> (0/1,1/0) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.