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 -8/1 -7/1 -6/1 -5/1 -13/3 -4/1 -11/3 -7/2 -10/3 -3/1 -12/5 -7/3 -2/1 -9/5 -7/4 -7/5 -7/6 -1/1 -7/8 -7/9 -7/10 -7/11 -7/12 -7/13 0/1 1/2 7/13 7/12 7/11 7/10 3/4 7/9 7/8 1/1 7/6 5/4 14/11 7/5 3/2 14/9 7/4 2/1 28/13 9/4 7/3 12/5 5/2 28/11 70/27 84/31 11/4 14/5 3/1 42/13 13/4 10/3 7/2 11/3 4/1 13/3 84/19 9/2 14/3 5/1 11/2 28/5 6/1 13/2 7/1 8/1 9/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -8/1 -1/1 -7/1 -2/1 0/1 -13/2 -2/1 -6/1 -1/1 -11/2 -2/1 -5/1 1/0 -14/3 -1/1 -9/2 0/1 -31/7 1/0 -22/5 -1/1 -13/3 -2/1 -4/1 -1/1 -15/4 -1/2 -26/7 -1/1 -11/3 -1/2 -7/2 0/1 -17/5 1/0 -27/8 1/0 -37/11 0/1 -10/3 -1/1 -13/4 1/0 -16/5 -1/1 -3/1 0/1 -14/5 0/1 -11/4 1/2 -19/7 1/0 -46/17 -1/1 -27/10 0/1 -8/3 1/1 -29/11 0/1 -21/8 0/1 -34/13 1/1 -13/5 1/0 -18/7 -1/1 -5/2 0/1 -17/7 0/1 -29/12 1/0 -12/5 -1/1 -7/3 0/1 -16/7 1/3 -25/11 0/1 -34/15 1/3 -9/4 1/2 -11/5 2/3 -13/6 0/1 -2/1 1/1 -15/8 1/0 -28/15 1/1 -13/7 2/1 -11/6 2/1 -9/5 1/0 -7/4 1/0 -19/11 1/0 -50/29 -1/1 -81/47 -2/1 -112/65 -2/1 -31/18 -2/1 -12/7 -1/1 -41/24 1/0 -70/41 0/1 -29/17 1/0 -17/10 0/1 -5/3 0/1 -28/17 0/1 -23/14 0/1 -18/11 1/1 -13/8 1/2 -34/21 1/1 -21/13 1/1 -29/18 4/3 -8/5 1/1 -27/17 2/1 -46/29 3/1 -65/41 1/0 -84/53 1/0 -19/12 1/0 -11/7 1/0 -14/9 1/0 -3/2 0/1 -16/11 1/1 -29/20 1/0 -42/29 1/0 -13/9 1/0 -10/7 1/1 -7/5 0/1 2/1 -18/13 1/1 -65/47 2/1 -112/81 1/0 -47/34 0/1 -29/21 1/0 -11/8 1/0 -26/19 1/1 -41/30 0/1 -56/41 1/1 -15/11 1/0 -4/3 1/1 -13/10 2/1 -22/17 -1/1 -53/41 1/0 -84/65 0/1 -31/24 1/0 -9/7 0/1 -14/11 1/1 -5/4 1/0 -11/9 2/1 -28/23 1/0 -17/14 0/1 -6/5 1/1 -13/11 2/1 -7/6 0/1 2/1 -8/7 1/1 -1/1 1/0 -7/8 1/0 -6/7 -1/1 -11/13 0/1 -5/6 0/1 -14/17 1/1 -9/11 0/1 -22/27 1/1 -13/16 1/0 -4/5 1/1 -15/19 1/0 -11/14 2/1 -7/9 0/1 2/1 -17/22 2/1 -27/35 1/0 -10/13 1/1 -13/17 1/0 -16/21 1/1 -3/4 1/0 -14/19 1/0 -11/15 1/0 -19/26 0/1 -27/37 0/1 -8/11 1/1 -21/29 1/0 -13/18 -2/1 -18/25 -1/1 -5/7 0/1 -17/24 1/0 -29/41 1/0 -12/17 1/1 -7/10 0/1 2/1 -16/23 1/1 -25/36 1/0 -9/13 1/0 -11/16 1/2 -2/3 1/1 -11/17 2/1 -9/14 0/1 -7/11 1/1 -19/30 4/3 -31/49 4/3 -12/19 1/1 -41/65 3/2 -70/111 3/2 -29/46 2/1 -17/27 4/3 -5/8 3/2 -28/45 2/1 -23/37 2/1 -18/29 1/1 -13/21 3/2 -21/34 2/1 -8/13 1/1 -27/44 3/2 -19/31 3/2 -11/18 2/1 -14/23 2/1 -3/5 2/1 -16/27 3/1 -29/49 1/0 -42/71 2/1 -13/22 2/1 -10/17 3/1 -7/12 1/0 -18/31 1/1 -29/50 2/1 -11/19 1/0 -15/26 2/1 -4/7 1/1 -13/23 2/1 -22/39 1/1 -9/16 1/0 -14/25 1/1 -5/9 3/2 -11/20 3/2 -28/51 3/2 -17/31 2/1 -6/11 5/3 -7/13 2/1 -1/2 2/1 0/1 1/0 1/2 -4/1 7/13 -3/1 6/11 -3/1 11/20 1/0 5/9 -4/1 9/16 1/0 13/23 -7/2 4/7 -3/1 11/19 -16/5 7/12 -3/1 17/29 -26/9 27/46 -20/7 10/17 -3/1 13/22 -8/3 3/5 -5/2 11/18 -2/1 8/13 -3/1 21/34 -4/1 -2/1 13/21 -2/1 5/8 1/0 12/19 -3/1 7/11 -4/1 -2/1 16/25 -3/1 9/14 -2/1 11/17 1/0 2/3 -3/1 9/13 -2/1 7/10 -2/1 19/27 -2/1 31/44 -3/2 12/17 -1/1 17/24 1/0 5/7 1/0 18/25 -1/1 13/18 -2/1 21/29 -2/1 0/1 8/11 -1/1 19/26 -2/1 11/15 0/1 3/4 1/0 10/13 -3/1 7/9 -3/1 18/23 -3/1 11/14 -2/1 15/19 -2/1 4/5 -3/1 9/11 1/0 5/6 -2/1 6/7 -3/1 7/8 -2/1 1/1 -2/1 8/7 -3/1 7/6 -2/1 13/11 -7/4 19/16 -3/2 6/5 -5/3 11/9 -3/2 27/22 -2/1 16/13 -1/1 5/4 -3/2 14/11 -1/1 23/18 -2/1 9/7 -3/2 31/24 -3/2 22/17 -1/1 13/10 -4/3 17/13 -6/5 4/3 -1/1 15/11 -4/3 26/19 -1/1 11/8 -5/4 7/5 -1/1 17/12 -5/6 44/31 -1/1 27/19 -4/5 37/26 -4/5 10/7 -1/1 33/23 -3/4 23/16 -1/2 13/9 -2/3 16/11 -1/1 3/2 0/1 14/9 1/0 25/16 1/0 11/7 -4/1 19/12 1/0 46/29 -3/1 27/17 1/0 8/5 -3/1 29/18 -2/1 21/13 -2/1 34/21 -9/5 13/8 -3/2 18/11 -1/1 5/3 -3/2 17/10 -4/3 46/27 -1/1 29/17 -4/3 12/7 -1/1 7/4 -1/1 16/9 -1/1 25/14 -2/3 34/19 -1/1 9/5 -2/3 20/11 -1/3 11/6 0/1 13/7 1/0 2/1 -1/1 15/7 0/1 28/13 -1/1 13/6 -2/3 11/5 -1/2 9/4 -1/2 7/3 0/1 19/8 1/2 50/21 1/1 81/34 0/1 112/47 0/1 31/13 1/2 43/18 0/1 55/23 0/1 12/5 1/1 41/17 2/1 70/29 1/0 29/12 1/0 17/7 1/0 39/16 1/0 22/9 -1/1 5/2 0/1 28/11 0/1 51/20 1/4 23/9 1/2 18/7 1/1 31/12 1/0 44/17 1/1 57/22 2/1 70/27 1/0 13/5 0/1 34/13 1/1 21/8 1/0 29/11 1/0 37/14 -2/1 8/3 -1/1 27/10 -2/3 46/17 -1/1 65/24 -1/2 84/31 -1/2 19/7 0/1 30/11 -1/1 11/4 -1/2 14/5 0/1 17/6 0/1 3/1 1/0 19/6 0/1 16/5 -1/1 29/9 0/1 71/22 0/1 42/13 0/1 13/4 1/0 10/3 -1/1 7/2 0/1 18/5 1/3 65/18 2/5 112/31 1/2 47/13 1/2 29/8 1/2 11/3 0/1 26/7 1/1 41/11 1/2 56/15 1/1 15/4 1/0 34/9 1/3 19/5 1/2 4/1 1/1 13/3 1/0 22/5 1/1 53/12 1/0 84/19 0/1 31/7 0/1 9/2 0/1 14/3 1/1 19/4 3/2 5/1 2/1 11/2 2/1 28/5 1/0 45/8 1/0 17/3 1/0 6/1 3/1 13/2 6/1 7/1 1/0 8/1 -3/1 9/1 0/1 1/0 1/0 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(27,224,-44,-365) (-8/1,1/0) -> (-8/13,-27/44) Hyperbolic Matrix(29,224,40,309) (-8/1,-7/1) -> (21/29,8/11) Hyperbolic Matrix(55,364,76,503) (-7/1,-13/2) -> (13/18,21/29) Hyperbolic Matrix(57,364,44,281) (-13/2,-6/1) -> (22/17,13/10) Hyperbolic Matrix(29,168,-24,-139) (-6/1,-11/2) -> (-17/14,-6/5) Hyperbolic Matrix(27,140,16,83) (-11/2,-5/1) -> (5/3,17/10) Hyperbolic Matrix(29,140,-52,-251) (-5/1,-14/3) -> (-14/25,-5/9) Hyperbolic Matrix(55,252,12,55) (-14/3,-9/2) -> (9/2,14/3) Hyperbolic Matrix(139,616,44,195) (-9/2,-31/7) -> (3/1,19/6) Hyperbolic Matrix(419,1848,-324,-1429) (-31/7,-22/5) -> (-22/17,-53/41) 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,-36,-139) (-4/1,-15/4) -> (-13/16,-4/5) Hyperbolic Matrix(113,420,-60,-223) (-15/4,-26/7) -> (-2/1,-15/8) Hyperbolic Matrix(83,308,128,475) (-26/7,-11/3) -> (11/17,2/3) 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(83,280,8,27) (-27/8,-37/11) -> (9/1,1/0) Hyperbolic Matrix(393,1316,-284,-951) (-37/11,-10/3) -> (-18/13,-65/47) Hyperbolic Matrix(111,364,68,223) (-10/3,-13/4) -> (13/8,18/11) Hyperbolic Matrix(253,812,-148,-475) (-13/4,-16/5) -> (-12/7,-41/24) Hyperbolic Matrix(167,532,-264,-841) (-16/5,-3/1) -> (-31/49,-12/19) Hyperbolic Matrix(29,84,-48,-139) (-3/1,-14/5) -> (-14/23,-3/5) Hyperbolic Matrix(111,308,40,111) (-14/5,-11/4) -> (11/4,14/5) Hyperbolic Matrix(113,308,-164,-447) (-11/4,-19/7) -> (-9/13,-11/16) Hyperbolic Matrix(1427,3864,-900,-2437) (-19/7,-46/17) -> (-46/29,-65/41) Hyperbolic Matrix(559,1512,952,2575) (-46/17,-27/10) -> (27/46,10/17) Hyperbolic Matrix(167,448,104,279) (-27/10,-8/3) -> (8/5,29/18) Hyperbolic Matrix(169,448,-232,-615) (-8/3,-29/11) -> (-27/37,-8/11) Hyperbolic Matrix(85,224,96,253) (-29/11,-21/8) -> (7/8,1/1) Hyperbolic Matrix(139,364,160,419) (-21/8,-34/13) -> (6/7,7/8) Hyperbolic Matrix(279,728,64,167) (-34/13,-13/5) -> (13/3,22/5) Hyperbolic Matrix(141,364,-184,-475) (-13/5,-18/7) -> (-10/13,-13/17) Hyperbolic Matrix(197,504,-120,-307) (-18/7,-5/2) -> (-23/14,-18/11) Hyperbolic Matrix(57,140,-68,-167) (-5/2,-17/7) -> (-11/13,-5/6) 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(83,196,-36,-85) (-12/5,-7/3) -> (-7/3,-16/7) Parabolic Matrix(197,448,-332,-755) (-16/7,-25/11) -> (-3/5,-16/27) Hyperbolic Matrix(1765,4004,-1024,-2323) (-25/11,-34/15) -> (-50/29,-81/47) Hyperbolic Matrix(309,700,260,589) (-34/15,-9/4) -> (19/16,6/5) Hyperbolic Matrix(139,308,88,195) (-9/4,-11/5) -> (11/7,19/12) Hyperbolic Matrix(167,364,128,279) (-11/5,-13/6) -> (13/10,17/13) Hyperbolic Matrix(197,420,-144,-307) (-13/6,-2/1) -> (-26/19,-41/30) Hyperbolic Matrix(673,1260,180,337) (-15/8,-28/15) -> (56/15,15/4) Hyperbolic Matrix(421,784,196,365) (-28/15,-13/7) -> (15/7,28/13) Hyperbolic Matrix(167,308,212,391) (-13/7,-11/6) -> (11/14,15/19) Hyperbolic Matrix(169,308,-276,-503) (-11/6,-9/5) -> (-19/31,-11/18) Hyperbolic Matrix(111,196,-64,-113) (-9/5,-7/4) -> (-7/4,-19/11) Parabolic Matrix(925,1596,244,421) (-19/11,-50/29) -> (34/9,19/5) Hyperbolic Matrix(5963,10276,1348,2323) (-81/47,-112/65) -> (84/19,31/7) Hyperbolic Matrix(7281,12544,3056,5265) (-112/65,-31/18) -> (81/34,112/47) Hyperbolic Matrix(309,532,212,365) (-31/18,-12/7) -> (16/11,3/2) Hyperbolic Matrix(1541,2632,476,813) (-41/24,-70/41) -> (42/13,13/4) Hyperbolic Matrix(1903,3248,-3216,-5489) (-70/41,-29/17) -> (-29/49,-42/71) Hyperbolic Matrix(559,952,-724,-1233) (-29/17,-17/10) -> (-17/22,-27/35) Hyperbolic Matrix(83,140,16,27) (-17/10,-5/3) -> (5/1,11/2) Hyperbolic Matrix(475,784,-764,-1261) (-5/3,-28/17) -> (-28/45,-23/37) Hyperbolic Matrix(477,784,188,309) (-28/17,-23/14) -> (5/2,28/11) Hyperbolic Matrix(223,364,68,111) (-18/11,-13/8) -> (13/4,10/3) Hyperbolic Matrix(449,728,-552,-895) (-13/8,-34/21) -> (-22/27,-13/16) Hyperbolic Matrix(225,364,416,673) (-34/21,-21/13) -> (7/13,6/11) Hyperbolic Matrix(139,224,260,419) (-21/13,-29/18) -> (1/2,7/13) Hyperbolic Matrix(279,448,104,167) (-29/18,-8/5) -> (8/3,27/10) Hyperbolic Matrix(141,224,124,197) (-8/5,-27/17) -> (1/1,8/7) Hyperbolic Matrix(1623,2576,952,1511) (-27/17,-46/29) -> (46/27,29/17) Hyperbolic Matrix(7083,11228,1960,3107) (-65/41,-84/53) -> (112/31,47/13) Hyperbolic Matrix(4453,7056,1644,2605) (-84/53,-19/12) -> (65/24,84/31) Hyperbolic Matrix(195,308,88,139) (-19/12,-11/7) -> (11/5,9/4) Hyperbolic Matrix(197,308,-268,-419) (-11/7,-14/9) -> (-14/19,-11/15) Hyperbolic Matrix(55,84,36,55) (-14/9,-3/2) -> (3/2,14/9) Hyperbolic Matrix(307,448,172,251) (-3/2,-16/11) -> (16/9,25/14) Hyperbolic Matrix(2241,3248,928,1345) (-29/20,-42/29) -> (70/29,29/12) Hyperbolic Matrix(1819,2632,-2884,-4173) (-42/29,-13/9) -> (-41/65,-70/111) Hyperbolic Matrix(253,364,-408,-587) (-13/9,-10/7) -> (-18/29,-13/21) Hyperbolic Matrix(139,196,-100,-141) (-10/7,-7/5) -> (-7/5,-18/13) Parabolic Matrix(5487,7588,2024,2799) (-65/47,-112/81) -> (84/31,19/7) Hyperbolic Matrix(9073,12544,2512,3473) (-112/81,-47/34) -> (65/18,112/31) Hyperbolic Matrix(1763,2436,668,923) (-47/34,-29/21) -> (29/11,37/14) Hyperbolic Matrix(589,812,-832,-1147) (-29/21,-11/8) -> (-17/24,-29/41) Hyperbolic Matrix(449,616,164,225) (-11/8,-26/19) -> (30/11,11/4) Hyperbolic Matrix(1373,1876,636,869) (-41/30,-56/41) -> (28/13,13/6) 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,-148,-195) (-4/3,-13/10) -> (-15/26,-4/7) 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(5461,7056,1236,1597) (-84/65,-31/24) -> (53/12,84/19) Hyperbolic Matrix(673,868,956,1233) (-31/24,-9/7) -> (19/27,31/44) Hyperbolic Matrix(197,252,-240,-307) (-9/7,-14/11) -> (-14/17,-9/11) Hyperbolic Matrix(111,140,88,111) (-14/11,-5/4) -> (5/4,14/11) Hyperbolic Matrix(113,140,-180,-223) (-5/4,-11/9) -> (-17/27,-5/8) Hyperbolic Matrix(643,784,-1172,-1429) (-11/9,-28/23) -> (-28/51,-17/31) Hyperbolic Matrix(645,784,116,141) (-28/23,-17/14) -> (11/2,28/5) Hyperbolic Matrix(307,364,-544,-645) (-6/5,-13/11) -> (-13/23,-22/39) Hyperbolic Matrix(309,364,500,589) (-13/11,-7/6) -> (21/34,13/21) Hyperbolic Matrix(195,224,316,363) (-7/6,-8/7) -> (8/13,21/34) Hyperbolic Matrix(197,224,124,141) (-8/7,-1/1) -> (27/17,8/5) Hyperbolic Matrix(253,224,96,85) (-1/1,-7/8) -> (21/8,29/11) Hyperbolic Matrix(419,364,160,139) (-7/8,-6/7) -> (34/13,21/8) Hyperbolic Matrix(197,168,-360,-307) (-6/7,-11/13) -> (-17/31,-6/11) Hyperbolic Matrix(475,392,372,307) (-5/6,-14/17) -> (14/11,23/18) Hyperbolic Matrix(617,504,344,281) (-9/11,-22/27) -> (34/19,9/5) Hyperbolic Matrix(141,112,248,197) (-4/5,-15/19) -> (13/23,4/7) Hyperbolic Matrix(391,308,212,167) (-15/19,-11/14) -> (11/6,13/7) Hyperbolic Matrix(251,196,-324,-253) (-11/14,-7/9) -> (-7/9,-17/22) Parabolic Matrix(1961,1512,1236,953) (-27/35,-10/13) -> (46/29,27/17) Hyperbolic Matrix(1065,812,-1688,-1287) (-13/17,-16/21) -> (-12/19,-41/65) Hyperbolic Matrix(699,532,992,755) (-16/21,-3/4) -> (31/44,12/17) Hyperbolic Matrix(531,392,340,251) (-3/4,-14/19) -> (14/9,25/16) Hyperbolic Matrix(421,308,652,477) (-11/15,-19/26) -> (9/14,11/17) Hyperbolic Matrix(2071,1512,1456,1063) (-19/26,-27/37) -> (27/19,37/26) Hyperbolic Matrix(309,224,40,29) (-8/11,-21/29) -> (7/1,8/1) Hyperbolic Matrix(503,364,76,55) (-21/29,-13/18) -> (13/2,7/1) Hyperbolic Matrix(505,364,856,617) (-13/18,-18/25) -> (10/17,13/22) Hyperbolic Matrix(701,504,-1128,-811) (-18/25,-5/7) -> (-23/37,-18/29) Hyperbolic Matrix(197,140,356,253) (-5/7,-17/24) -> (11/20,5/9) Hyperbolic Matrix(1149,812,-1940,-1371) (-29/41,-12/17) -> (-16/27,-29/49) Hyperbolic Matrix(279,196,-400,-281) (-12/17,-7/10) -> (-7/10,-16/23) Parabolic Matrix(2297,1596,888,617) (-16/23,-25/36) -> (31/12,44/17) Hyperbolic Matrix(727,504,564,391) (-25/36,-9/13) -> (9/7,31/24) Hyperbolic Matrix(449,308,328,225) (-11/16,-2/3) -> (26/19,11/8) Hyperbolic Matrix(475,308,128,83) (-2/3,-11/17) -> (11/3,26/7) Hyperbolic Matrix(477,308,652,421) (-11/17,-9/14) -> (19/26,11/15) Hyperbolic Matrix(307,196,-484,-309) (-9/14,-7/11) -> (-7/11,-19/30) Parabolic Matrix(1371,868,308,195) (-19/30,-31/49) -> (31/7,9/2) Hyperbolic Matrix(9547,6020,3684,2323) (-70/111,-29/46) -> (57/22,70/27) Hyperbolic Matrix(1511,952,2576,1623) (-29/46,-17/27) -> (17/29,27/46) Hyperbolic Matrix(2519,1568,988,615) (-5/8,-28/45) -> (28/11,51/20) Hyperbolic Matrix(589,364,500,309) (-13/21,-21/34) -> (7/6,13/11) Hyperbolic Matrix(363,224,316,195) (-21/34,-8/13) -> (8/7,7/6) Hyperbolic Matrix(2967,1820,820,503) (-27/44,-19/31) -> (47/13,29/8) Hyperbolic Matrix(643,392,228,139) (-11/18,-14/23) -> (14/5,17/6) Hyperbolic Matrix(5965,3528,1848,1093) (-42/71,-13/22) -> (71/22,42/13) Hyperbolic Matrix(617,364,856,505) (-13/22,-10/17) -> (18/25,13/18) Hyperbolic Matrix(335,196,-576,-337) (-10/17,-7/12) -> (-7/12,-18/31) Parabolic Matrix(3137,1820,1160,673) (-18/31,-29/50) -> (27/10,46/17) Hyperbolic Matrix(1063,616,868,503) (-29/50,-11/19) -> (11/9,27/22) Hyperbolic Matrix(533,308,244,141) (-11/19,-15/26) -> (13/6,11/5) Hyperbolic Matrix(197,112,248,141) (-4/7,-13/23) -> (15/19,4/5) Hyperbolic Matrix(1541,868,648,365) (-22/39,-9/16) -> (19/8,50/21) Hyperbolic Matrix(699,392,148,83) (-9/16,-14/25) -> (14/3,19/4) Hyperbolic Matrix(253,140,356,197) (-5/9,-11/20) -> (17/24,5/7) Hyperbolic Matrix(2855,1568,508,279) (-11/20,-28/51) -> (28/5,45/8) Hyperbolic Matrix(673,364,416,225) (-6/11,-7/13) -> (21/13,34/21) Hyperbolic Matrix(419,224,260,139) (-7/13,-1/2) -> (29/18,21/13) Hyperbolic Matrix(1,0,4,1) (-1/2,0/1) -> (0/1,1/2) Parabolic Matrix(869,-476,356,-195) (6/11,11/20) -> (39/16,22/9) Hyperbolic Matrix(251,-140,52,-29) (5/9,9/16) -> (19/4,5/1) Hyperbolic Matrix(645,-364,544,-307) (9/16,13/23) -> (13/11,19/16) Hyperbolic Matrix(195,-112,148,-85) (4/7,11/19) -> (17/13,4/3) Hyperbolic Matrix(337,-196,576,-335) (11/19,7/12) -> (7/12,17/29) Parabolic Matrix(897,-532,376,-223) (13/22,3/5) -> (31/13,43/18) Hyperbolic Matrix(139,-84,48,-29) (3/5,11/18) -> (17/6,3/1) Hyperbolic Matrix(503,-308,276,-169) (11/18,8/13) -> (20/11,11/6) Hyperbolic Matrix(587,-364,408,-253) (13/21,5/8) -> (23/16,13/9) Hyperbolic Matrix(223,-140,180,-113) (5/8,12/19) -> (16/13,5/4) Hyperbolic Matrix(309,-196,484,-307) (12/19,7/11) -> (7/11,16/25) Parabolic Matrix(699,-448,220,-141) (16/25,9/14) -> (19/6,16/5) Hyperbolic Matrix(447,-308,164,-113) (2/3,9/13) -> (19/7,30/11) Hyperbolic Matrix(281,-196,400,-279) (9/13,7/10) -> (7/10,19/27) Parabolic Matrix(1345,-952,948,-671) (12/17,17/24) -> (17/12,44/31) Hyperbolic Matrix(895,-644,624,-449) (5/7,18/25) -> (10/7,33/23) Hyperbolic Matrix(615,-448,232,-169) (8/11,19/26) -> (37/14,8/3) Hyperbolic Matrix(419,-308,268,-197) (11/15,3/4) -> (25/16,11/7) Hyperbolic Matrix(475,-364,184,-141) (3/4,10/13) -> (18/7,31/12) Hyperbolic Matrix(253,-196,324,-251) (10/13,7/9) -> (7/9,18/23) Parabolic Matrix(1035,-812,608,-477) (18/23,11/14) -> (17/10,46/27) Hyperbolic Matrix(139,-112,36,-29) (4/5,9/11) -> (19/5,4/1) Hyperbolic Matrix(307,-252,240,-197) (9/11,5/6) -> (23/18,9/7) Hyperbolic Matrix(167,-140,68,-57) (5/6,6/7) -> (22/9,5/2) Hyperbolic Matrix(139,-168,24,-29) (6/5,11/9) -> (17/3,6/1) Hyperbolic Matrix(1709,-2100,660,-811) (27/22,16/13) -> (44/17,57/22) Hyperbolic Matrix(1429,-1848,324,-419) (31/24,22/17) -> (22/5,53/12) Hyperbolic Matrix(307,-420,144,-197) (15/11,26/19) -> (2/1,15/7) Hyperbolic Matrix(141,-196,100,-139) (11/8,7/5) -> (7/5,17/12) Parabolic Matrix(1933,-2744,808,-1147) (44/31,27/19) -> (55/23,12/5) Hyperbolic Matrix(923,-1316,256,-365) (37/26,10/7) -> (18/5,65/18) Hyperbolic Matrix(1541,-2212,604,-867) (33/23,23/16) -> (51/20,23/9) Hyperbolic Matrix(559,-812,232,-337) (13/9,16/11) -> (12/5,41/17) Hyperbolic Matrix(2437,-3864,900,-1427) (19/12,46/29) -> (46/17,65/24) Hyperbolic Matrix(587,-952,156,-253) (34/21,13/8) -> (15/4,34/9) Hyperbolic Matrix(307,-504,120,-197) (18/11,5/3) -> (23/9,18/7) Hyperbolic Matrix(475,-812,148,-253) (29/17,12/7) -> (16/5,29/9) Hyperbolic Matrix(113,-196,64,-111) (12/7,7/4) -> (7/4,16/9) Parabolic Matrix(2239,-4004,940,-1681) (25/14,34/19) -> (50/21,81/34) Hyperbolic Matrix(139,-252,16,-29) (9/5,20/11) -> (8/1,9/1) Hyperbolic Matrix(223,-420,60,-113) (13/7,2/1) -> (26/7,41/11) Hyperbolic Matrix(85,-196,36,-83) (9/4,7/3) -> (7/3,19/8) Parabolic Matrix(2155,-5152,668,-1597) (43/18,55/23) -> (29/9,71/22) Hyperbolic Matrix(1567,-3780,604,-1457) (41/17,70/29) -> (70/27,13/5) Hyperbolic Matrix(587,-1428,104,-253) (17/7,39/16) -> (45/8,17/3) Hyperbolic Matrix(57,-196,16,-55) (10/3,7/2) -> (7/2,18/5) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(27,224,-44,-365) -> Matrix(3,4,2,3) Matrix(29,224,40,309) -> Matrix(1,0,0,1) Matrix(55,364,76,503) -> Matrix(1,0,0,1) Matrix(57,364,44,281) -> Matrix(3,2,-2,-1) Matrix(29,168,-24,-139) -> Matrix(1,2,0,1) Matrix(27,140,16,83) -> Matrix(3,2,-2,-1) Matrix(29,140,-52,-251) -> Matrix(3,4,2,3) Matrix(55,252,12,55) -> Matrix(1,0,2,1) Matrix(139,616,44,195) -> Matrix(1,0,0,1) Matrix(419,1848,-324,-1429) -> Matrix(1,0,0,1) Matrix(167,728,64,279) -> Matrix(1,2,0,1) Matrix(27,112,20,83) -> Matrix(3,2,-2,-1) Matrix(29,112,-36,-139) -> Matrix(1,0,2,1) Matrix(113,420,-60,-223) -> Matrix(1,0,2,1) Matrix(83,308,128,475) -> Matrix(7,4,-2,-1) Matrix(55,196,-16,-57) -> Matrix(1,0,2,1) Matrix(281,952,116,393) -> Matrix(1,0,0,1) Matrix(83,280,8,27) -> Matrix(1,0,0,1) Matrix(393,1316,-284,-951) -> Matrix(1,2,0,1) Matrix(111,364,68,223) -> Matrix(3,2,-2,-1) Matrix(253,812,-148,-475) -> Matrix(1,0,0,1) Matrix(167,532,-264,-841) -> Matrix(3,4,2,3) Matrix(29,84,-48,-139) -> Matrix(1,2,0,1) Matrix(111,308,40,111) -> Matrix(1,0,-4,1) Matrix(113,308,-164,-447) -> Matrix(1,0,0,1) Matrix(1427,3864,-900,-2437) -> Matrix(1,4,0,1) Matrix(559,1512,952,2575) -> Matrix(17,20,-6,-7) Matrix(167,448,104,279) -> Matrix(5,-2,-2,1) Matrix(169,448,-232,-615) -> Matrix(1,0,0,1) Matrix(85,224,96,253) -> Matrix(1,-2,0,1) Matrix(139,364,160,419) -> Matrix(5,-2,-2,1) Matrix(279,728,64,167) -> Matrix(1,0,0,1) Matrix(141,364,-184,-475) -> Matrix(1,2,0,1) Matrix(197,504,-120,-307) -> Matrix(1,0,2,1) Matrix(57,140,-68,-167) -> Matrix(1,0,0,1) Matrix(335,812,92,223) -> Matrix(1,0,2,1) Matrix(337,812,-232,-559) -> Matrix(1,2,0,1) Matrix(83,196,-36,-85) -> Matrix(1,0,4,1) Matrix(197,448,-332,-755) -> Matrix(3,-2,2,-1) Matrix(1765,4004,-1024,-2323) -> Matrix(5,-2,-2,1) Matrix(309,700,260,589) -> Matrix(1,-2,0,1) Matrix(139,308,88,195) -> Matrix(5,-2,-2,1) Matrix(167,364,128,279) -> Matrix(3,-4,-2,3) Matrix(197,420,-144,-307) -> Matrix(1,0,0,1) Matrix(673,1260,180,337) -> Matrix(1,0,0,1) Matrix(421,784,196,365) -> Matrix(1,-2,0,1) Matrix(167,308,212,391) -> Matrix(1,-4,0,1) Matrix(169,308,-276,-503) -> Matrix(3,-8,2,-5) Matrix(111,196,-64,-113) -> Matrix(1,-4,0,1) Matrix(925,1596,244,421) -> Matrix(1,2,2,5) Matrix(5963,10276,1348,2323) -> Matrix(1,2,0,1) Matrix(7281,12544,3056,5265) -> Matrix(1,2,0,1) Matrix(309,532,212,365) -> Matrix(1,2,-2,-3) Matrix(1541,2632,476,813) -> Matrix(1,0,0,1) Matrix(1903,3248,-3216,-5489) -> Matrix(1,2,0,1) Matrix(559,952,-724,-1233) -> Matrix(1,2,0,1) Matrix(83,140,16,27) -> Matrix(1,2,0,1) Matrix(475,784,-764,-1261) -> Matrix(1,2,0,1) Matrix(477,784,188,309) -> Matrix(1,0,-2,1) Matrix(223,364,68,111) -> Matrix(1,0,-2,1) Matrix(449,728,-552,-895) -> Matrix(3,-2,2,-1) Matrix(225,364,416,673) -> Matrix(11,-8,-4,3) Matrix(139,224,260,419) -> Matrix(13,-16,-4,5) Matrix(279,448,104,167) -> Matrix(1,-2,0,1) Matrix(141,224,124,197) -> Matrix(1,-4,0,1) Matrix(1623,2576,952,1511) -> Matrix(3,-10,-2,7) Matrix(7083,11228,1960,3107) -> Matrix(1,-4,2,-7) Matrix(4453,7056,1644,2605) -> Matrix(1,0,-2,1) Matrix(195,308,88,139) -> Matrix(1,-2,-2,5) Matrix(197,308,-268,-419) -> Matrix(1,-4,0,1) Matrix(55,84,36,55) -> Matrix(1,0,0,1) Matrix(307,448,172,251) -> Matrix(3,-2,-4,3) Matrix(2241,3248,928,1345) -> Matrix(1,-2,0,1) Matrix(1819,2632,-2884,-4173) -> Matrix(3,4,2,3) Matrix(253,364,-408,-587) -> Matrix(3,-2,2,-1) Matrix(139,196,-100,-141) -> Matrix(1,0,0,1) Matrix(5487,7588,2024,2799) -> Matrix(1,-2,-2,5) Matrix(9073,12544,2512,3473) -> Matrix(1,2,2,5) Matrix(1763,2436,668,923) -> Matrix(1,-2,0,1) Matrix(589,812,-832,-1147) -> Matrix(1,0,0,1) Matrix(449,616,164,225) -> Matrix(1,0,-2,1) Matrix(1373,1876,636,869) -> Matrix(3,-2,-4,3) Matrix(2297,3136,616,841) -> Matrix(1,-2,2,-3) Matrix(83,112,20,27) -> Matrix(1,0,0,1) Matrix(85,112,-148,-195) -> Matrix(1,0,0,1) Matrix(281,364,44,57) -> Matrix(1,4,0,1) Matrix(6607,8540,2772,3583) -> Matrix(1,0,2,1) Matrix(5461,7056,1236,1597) -> Matrix(1,0,0,1) Matrix(673,868,956,1233) -> Matrix(3,2,-2,-1) Matrix(197,252,-240,-307) -> Matrix(1,0,0,1) Matrix(111,140,88,111) -> Matrix(3,-4,-2,3) Matrix(113,140,-180,-223) -> Matrix(3,-2,2,-1) Matrix(643,784,-1172,-1429) -> Matrix(3,-8,2,-5) Matrix(645,784,116,141) -> Matrix(1,2,0,1) Matrix(307,364,-544,-645) -> Matrix(1,0,0,1) Matrix(309,364,500,589) -> Matrix(1,-4,0,1) Matrix(195,224,316,363) -> Matrix(1,-4,0,1) Matrix(197,224,124,141) -> Matrix(1,-4,0,1) Matrix(253,224,96,85) -> Matrix(1,-2,0,1) Matrix(419,364,160,139) -> Matrix(1,2,0,1) Matrix(197,168,-360,-307) -> Matrix(3,-2,2,-1) Matrix(475,392,372,307) -> Matrix(1,-2,0,1) Matrix(617,504,344,281) -> Matrix(3,-2,-4,3) Matrix(141,112,248,197) -> Matrix(7,-10,-2,3) Matrix(391,308,212,167) -> Matrix(1,-2,0,1) Matrix(251,196,-324,-253) -> Matrix(1,0,0,1) Matrix(1961,1512,1236,953) -> Matrix(1,-4,0,1) Matrix(1065,812,-1688,-1287) -> Matrix(3,-2,2,-1) Matrix(699,532,992,755) -> Matrix(3,-4,-2,3) Matrix(531,392,340,251) -> Matrix(1,-8,0,1) Matrix(421,308,652,477) -> Matrix(1,-2,0,1) Matrix(2071,1512,1456,1063) -> Matrix(3,4,-4,-5) Matrix(309,224,40,29) -> Matrix(1,-4,0,1) Matrix(503,364,76,55) -> Matrix(1,8,0,1) Matrix(505,364,856,617) -> Matrix(11,14,-4,-5) Matrix(701,504,-1128,-811) -> Matrix(1,2,0,1) Matrix(197,140,356,253) -> Matrix(1,-4,0,1) Matrix(1149,812,-1940,-1371) -> Matrix(1,2,0,1) Matrix(279,196,-400,-281) -> Matrix(1,0,0,1) Matrix(2297,1596,888,617) -> Matrix(1,0,0,1) Matrix(727,504,564,391) -> Matrix(3,-4,-2,3) Matrix(449,308,328,225) -> Matrix(3,-4,-2,3) Matrix(475,308,128,83) -> Matrix(1,-2,2,-3) Matrix(477,308,652,421) -> Matrix(1,-2,0,1) Matrix(307,196,-484,-309) -> Matrix(5,-4,4,-3) Matrix(1371,868,308,195) -> Matrix(3,-4,4,-5) Matrix(9547,6020,3684,2323) -> Matrix(5,-8,2,-3) Matrix(1511,952,2576,1623) -> Matrix(17,-14,-6,5) Matrix(2519,1568,988,615) -> Matrix(1,-2,6,-11) Matrix(589,364,500,309) -> Matrix(11,-20,-6,11) Matrix(363,224,316,195) -> Matrix(1,-4,0,1) Matrix(2967,1820,820,503) -> Matrix(1,-2,4,-7) Matrix(643,392,228,139) -> Matrix(1,-2,6,-11) Matrix(5965,3528,1848,1093) -> Matrix(1,-2,-2,5) Matrix(617,364,856,505) -> Matrix(1,-4,0,1) Matrix(335,196,-576,-337) -> Matrix(1,-2,0,1) Matrix(3137,1820,1160,673) -> Matrix(1,0,-2,1) Matrix(1063,616,868,503) -> Matrix(3,-4,-2,3) Matrix(533,308,244,141) -> Matrix(1,0,-2,1) Matrix(197,112,248,141) -> Matrix(1,-4,0,1) Matrix(1541,868,648,365) -> Matrix(1,-2,2,-3) Matrix(699,392,148,83) -> Matrix(3,-2,2,-1) Matrix(253,140,356,197) -> Matrix(3,-4,-2,3) Matrix(2855,1568,508,279) -> Matrix(1,-2,2,-3) Matrix(673,364,416,225) -> Matrix(15,-28,-8,15) Matrix(419,224,260,139) -> Matrix(9,-20,-4,9) Matrix(1,0,4,1) -> Matrix(1,-6,0,1) Matrix(869,-476,356,-195) -> Matrix(1,2,0,1) Matrix(251,-140,52,-29) -> Matrix(3,10,2,7) Matrix(645,-364,544,-307) -> Matrix(3,14,-2,-9) Matrix(195,-112,148,-85) -> Matrix(1,2,0,1) Matrix(337,-196,576,-335) -> Matrix(41,126,-14,-43) Matrix(897,-532,376,-223) -> Matrix(3,8,4,11) Matrix(139,-84,48,-29) -> Matrix(1,2,2,5) Matrix(503,-308,276,-169) -> Matrix(1,2,-2,-3) Matrix(587,-364,408,-253) -> Matrix(1,4,-2,-7) Matrix(223,-140,180,-113) -> Matrix(3,8,-2,-5) Matrix(309,-196,484,-307) -> Matrix(1,0,0,1) Matrix(699,-448,220,-141) -> Matrix(1,2,0,1) Matrix(447,-308,164,-113) -> Matrix(1,2,0,1) Matrix(281,-196,400,-279) -> Matrix(7,16,-4,-9) Matrix(1345,-952,948,-671) -> Matrix(5,6,-6,-7) Matrix(895,-644,624,-449) -> Matrix(3,4,-4,-5) Matrix(615,-448,232,-169) -> Matrix(1,0,0,1) Matrix(419,-308,268,-197) -> Matrix(1,-4,0,1) Matrix(475,-364,184,-141) -> Matrix(1,4,0,1) Matrix(253,-196,324,-251) -> Matrix(5,18,-2,-7) Matrix(1035,-812,608,-477) -> Matrix(5,14,-4,-11) Matrix(139,-112,36,-29) -> Matrix(1,2,2,5) Matrix(307,-252,240,-197) -> Matrix(3,8,-2,-5) Matrix(167,-140,68,-57) -> Matrix(1,2,0,1) Matrix(139,-168,24,-29) -> Matrix(3,4,2,3) Matrix(1709,-2100,660,-811) -> Matrix(3,4,2,3) Matrix(1429,-1848,324,-419) -> Matrix(3,4,2,3) Matrix(307,-420,144,-197) -> Matrix(3,4,-4,-5) Matrix(141,-196,100,-139) -> Matrix(9,10,-10,-11) Matrix(1933,-2744,808,-1147) -> Matrix(5,4,6,5) Matrix(923,-1316,256,-365) -> Matrix(3,2,10,7) Matrix(1541,-2212,604,-867) -> Matrix(3,2,10,7) Matrix(559,-812,232,-337) -> Matrix(1,0,2,1) Matrix(2437,-3864,900,-1427) -> Matrix(1,4,-2,-7) Matrix(587,-952,156,-253) -> Matrix(1,2,-2,-3) Matrix(307,-504,120,-197) -> Matrix(1,2,0,1) Matrix(475,-812,148,-253) -> Matrix(3,4,-4,-5) Matrix(113,-196,64,-111) -> Matrix(7,8,-8,-9) Matrix(2239,-4004,940,-1681) -> Matrix(3,2,4,3) Matrix(139,-252,16,-29) -> Matrix(3,2,-2,-1) Matrix(223,-420,60,-113) -> Matrix(1,0,2,1) Matrix(85,-196,36,-83) -> Matrix(1,0,4,1) Matrix(2155,-5152,668,-1597) -> Matrix(1,0,-2,1) Matrix(1567,-3780,604,-1457) -> Matrix(1,-2,0,1) Matrix(587,-1428,104,-253) -> Matrix(1,2,0,1) Matrix(57,-196,16,-55) -> 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): 42 Degree of the the map X: 42 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. ----------------------------------------------------------------------- The image of the modular group liftables in PSL(2,Z) equals the image of the pure modular group liftables. ----------------------------------------------------------------------- The image of the extended modular group liftables in PGL(2,Z) equals the image of the modular liftables. ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.