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): 768 Minimal number of generators: 129 Number of equivalence classes of cusps: 64 Genus: 33 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -8/1 -7/1 -6/1 -5/1 -9/2 -4/1 -11/3 -10/3 -3/1 -8/3 -9/4 -2/1 -9/5 -3/2 -10/7 -4/3 -6/5 -1/1 -6/7 -3/4 -2/3 -3/5 -6/11 0/1 1/2 6/11 3/5 2/3 3/4 9/11 6/7 1/1 6/5 5/4 4/3 10/7 3/2 36/23 12/7 7/4 9/5 2/1 24/11 9/4 12/5 5/2 8/3 11/4 3/1 36/11 10/3 24/7 7/2 11/3 4/1 9/2 24/5 5/1 11/2 6/1 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 -2/1 -7/1 -2/1 -1/1 1/0 -6/1 -3/1 -1/1 -11/2 -2/1 -5/1 -3/1 -2/1 1/0 -14/3 -3/1 -23/5 -3/1 -5/2 -2/1 -9/2 -2/1 -13/3 -2/1 -5/3 -3/2 -4/1 -2/1 -15/4 -3/2 -11/3 -2/1 -3/2 -1/1 -18/5 -1/1 -7/2 -2/1 -24/7 -3/2 -17/5 -3/2 -7/5 -4/3 -10/3 -7/5 -1/1 -3/1 -1/1 -14/5 -1/1 -1/3 -25/9 -1/2 -1/3 0/1 -36/13 0/1 -11/4 1/0 -8/3 1/0 -13/5 -3/1 -2/1 1/0 -18/7 -3/1 -1/1 -5/2 -2/1 -12/5 -1/1 -7/3 -2/1 -3/2 -1/1 -23/10 0/1 -16/7 -2/1 -25/11 -2/1 -1/1 1/0 -9/4 -3/2 -11/5 -3/2 -4/3 -1/1 -2/1 -1/1 -13/7 -1/1 -3/4 -2/3 -24/13 -1/1 -11/6 -2/3 -9/5 -1/1 -25/14 -2/3 -16/9 -2/3 -23/13 -2/3 -3/5 -1/2 -7/4 -1/2 -12/7 -1/1 -5/3 -1/1 -1/2 0/1 -18/11 -1/1 -13/8 -3/4 -8/5 -1/2 -11/7 -1/1 -2/3 -1/2 -3/2 0/1 -13/9 1/1 2/1 1/0 -36/25 1/0 -23/16 1/0 -10/7 -1/1 1/1 -17/12 1/0 -24/17 1/0 -7/5 -2/1 -1/1 1/0 -18/13 -1/1 -11/8 1/0 -15/11 -1/1 1/1 -4/3 1/0 -13/10 -2/1 -9/7 -3/1 -1/1 -23/18 0/1 -14/11 -3/1 -19/15 -3/1 -2/1 1/0 -24/19 -2/1 -5/4 -3/2 -11/9 -5/4 -6/5 -1/1 -6/5 -1/1 -7/6 -2/3 -8/7 -2/3 -1/1 -1/1 0/1 1/0 -7/8 1/0 -6/7 -1/1 1/1 -5/6 0/1 -14/17 1/3 1/1 -23/28 1/2 -9/11 1/1 -4/5 1/0 -11/14 2/1 -18/23 1/1 3/1 -7/9 2/1 3/1 1/0 -10/13 3/1 -3/4 1/0 -14/19 -7/1 -25/34 -4/1 -36/49 1/0 -11/15 -7/1 -6/1 1/0 -8/11 1/0 -13/18 -4/1 -5/7 -4/1 -3/1 1/0 -12/17 -3/1 -7/10 -2/1 -16/23 -2/1 -25/36 1/0 -9/13 -3/1 -1/1 -11/16 1/0 -2/3 -3/1 -1/1 -13/20 1/0 -24/37 -3/1 -11/17 -3/1 -5/2 -2/1 -9/14 -2/1 -25/39 -2/1 -9/5 -7/4 -16/25 -2/1 -7/11 -2/1 -3/2 -1/1 -12/19 -1/1 -5/8 1/0 -13/21 -1/1 0/1 1/0 -8/13 1/0 -11/18 -2/1 -3/5 -3/1 -1/1 -13/22 -2/1 -36/61 -2/1 -23/39 -2/1 -7/4 -5/3 -10/17 -1/1 -7/12 1/0 -18/31 -3/1 -1/1 -11/19 -3/1 -2/1 1/0 -4/7 -2/1 -9/16 1/0 -23/41 -3/1 -5/2 -2/1 -14/25 -3/1 -1/1 -19/34 -2/1 -24/43 -2/1 -5/9 -2/1 -3/2 -1/1 -6/11 -1/1 -7/13 -2/1 -1/1 1/0 -1/2 -2/1 0/1 -1/1 1/2 0/1 6/11 -1/1 5/9 -1/1 -3/4 -2/3 14/25 -3/5 9/16 -1/2 4/7 0/1 11/19 0/1 1/1 1/0 7/12 1/0 10/17 -3/1 -1/1 3/5 -1/1 14/23 -1/1 -5/7 25/41 -5/7 -7/10 -2/3 11/18 -2/3 8/13 -1/2 5/8 -1/2 7/11 -1/1 -1/2 0/1 16/25 0/1 9/14 0/1 2/3 -1/1 9/13 -1/1 16/23 -2/3 7/10 -2/3 5/7 -1/1 -2/3 -1/2 13/18 -2/3 8/11 -1/2 3/4 -1/2 10/13 -1/1 -1/3 7/9 -1/2 -1/3 0/1 11/14 0/1 4/5 -1/2 9/11 -1/1 -1/3 14/17 -1/3 19/23 -1/5 -1/6 0/1 5/6 0/1 6/7 -1/1 -1/3 7/8 -1/2 1/1 -1/1 -1/2 0/1 8/7 0/1 7/6 0/1 6/5 -1/1 11/9 -1/1 -2/3 -1/2 5/4 -1/2 14/11 -1/1 1/1 23/18 -2/1 9/7 -1/1 13/10 -2/3 4/3 -1/2 15/11 -1/3 26/19 -1/3 11/8 -1/2 18/13 -1/3 25/18 -4/13 7/5 -1/3 -2/7 -1/4 24/17 -1/4 17/12 -1/4 10/7 -1/5 3/2 0/1 14/9 1/5 39/25 1/5 3/13 25/16 1/4 36/23 1/4 11/7 1/4 2/7 1/3 19/12 1/2 8/5 1/2 13/8 1/2 18/11 1/1 5/3 0/1 1/2 1/1 17/10 0/1 12/7 1/1 7/4 1/0 23/13 -1/1 0/1 1/0 16/9 0/1 25/14 2/1 9/5 -1/1 1/1 11/6 0/1 2/1 -1/1 1/1 13/6 0/1 24/11 1/1 11/5 1/1 2/1 1/0 9/4 1/0 34/15 -5/1 25/11 -4/1 -7/2 -3/1 16/7 -2/1 23/10 -2/1 7/3 -2/1 -1/1 1/0 19/8 1/0 12/5 -1/1 5/2 0/1 18/7 -1/1 1/1 31/12 1/0 13/5 0/1 1/1 1/0 60/23 1/0 47/18 -2/1 34/13 -1/1 1/1 21/8 1/0 8/3 1/0 11/4 -1/2 3/1 -1/1 1/1 13/4 -1/2 36/11 0/1 59/18 0/1 23/7 0/1 1/1 1/0 10/3 1/1 17/5 0/1 1/1 1/0 24/7 1/0 7/2 -2/1 18/5 -1/1 11/3 -1/1 -1/2 0/1 15/4 -1/2 4/1 0/1 13/3 -1/1 0/1 1/0 48/11 -1/1 35/8 1/0 22/5 -1/1 9/2 0/1 32/7 0/1 23/5 -1/1 0/1 1/0 14/3 -1/1 1/1 19/4 -1/2 24/5 0/1 29/6 0/1 5/1 0/1 1/1 1/0 11/2 0/1 6/1 -1/1 1/1 13/2 0/1 7/1 -1/1 0/1 1/0 8/1 0/1 9/1 1/1 1/0 1/0 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(25,216,-36,-311) (-8/1,1/0) -> (-16/23,-25/36) Hyperbolic Matrix(23,168,36,263) (-8/1,-7/1) -> (7/11,16/25) Hyperbolic Matrix(25,168,-32,-215) (-7/1,-6/1) -> (-18/23,-7/9) Hyperbolic Matrix(47,264,-60,-337) (-6/1,-11/2) -> (-11/14,-18/23) Hyperbolic Matrix(23,120,32,167) (-11/2,-5/1) -> (5/7,13/18) Hyperbolic Matrix(71,336,-56,-265) (-5/1,-14/3) -> (-14/11,-19/15) Hyperbolic Matrix(119,552,36,167) (-14/3,-23/5) -> (23/7,10/3) Hyperbolic Matrix(95,432,-148,-673) (-23/5,-9/2) -> (-9/14,-25/39) Hyperbolic Matrix(49,216,-76,-335) (-9/2,-13/3) -> (-11/17,-9/14) Hyperbolic Matrix(23,96,40,167) (-13/3,-4/1) -> (4/7,11/19) Hyperbolic Matrix(25,96,44,169) (-4/1,-15/4) -> (9/16,4/7) Hyperbolic Matrix(71,264,32,119) (-15/4,-11/3) -> (11/5,9/4) Hyperbolic Matrix(73,264,60,217) (-11/3,-18/5) -> (6/5,11/9) Hyperbolic Matrix(47,168,40,143) (-18/5,-7/2) -> (7/6,6/5) Hyperbolic Matrix(97,336,28,97) (-7/2,-24/7) -> (24/7,7/2) Hyperbolic Matrix(169,576,120,409) (-24/7,-17/5) -> (7/5,24/17) Hyperbolic Matrix(71,240,92,311) (-17/5,-10/3) -> (10/13,7/9) Hyperbolic Matrix(23,72,-8,-25) (-10/3,-3/1) -> (-3/1,-14/5) Parabolic Matrix(241,672,52,145) (-14/5,-25/9) -> (23/5,14/3) Hyperbolic Matrix(623,1728,-1056,-2929) (-25/9,-36/13) -> (-36/61,-23/39) Hyperbolic Matrix(313,864,96,265) (-36/13,-11/4) -> (13/4,36/11) Hyperbolic Matrix(71,192,44,119) (-11/4,-8/3) -> (8/5,13/8) Hyperbolic Matrix(73,192,-100,-263) (-8/3,-13/5) -> (-11/15,-8/11) Hyperbolic Matrix(167,432,-288,-745) (-13/5,-18/7) -> (-18/31,-11/19) Hyperbolic Matrix(47,120,56,143) (-18/7,-5/2) -> (5/6,6/7) Hyperbolic Matrix(49,120,20,49) (-5/2,-12/5) -> (12/5,5/2) Hyperbolic Matrix(71,168,-112,-265) (-12/5,-7/3) -> (-7/11,-12/19) Hyperbolic Matrix(145,336,104,241) (-7/3,-23/10) -> (25/18,7/5) Hyperbolic Matrix(335,768,188,431) (-23/10,-16/7) -> (16/9,25/14) Hyperbolic Matrix(95,216,84,191) (-16/7,-25/11) -> (1/1,8/7) Hyperbolic Matrix(191,432,-340,-769) (-25/11,-9/4) -> (-9/16,-23/41) Hyperbolic Matrix(119,264,32,71) (-9/4,-11/5) -> (11/3,15/4) Hyperbolic Matrix(23,48,-12,-25) (-11/5,-2/1) -> (-2/1,-13/7) Parabolic Matrix(311,576,-480,-889) (-13/7,-24/13) -> (-24/37,-11/17) Hyperbolic Matrix(313,576,144,265) (-24/13,-11/6) -> (13/6,24/11) Hyperbolic Matrix(119,216,92,167) (-11/6,-9/5) -> (9/7,13/10) Hyperbolic Matrix(241,432,188,337) (-9/5,-25/14) -> (23/18,9/7) Hyperbolic Matrix(431,768,188,335) (-25/14,-16/9) -> (16/7,23/10) Hyperbolic Matrix(433,768,-676,-1199) (-16/9,-23/13) -> (-25/39,-16/25) Hyperbolic Matrix(95,168,108,191) (-23/13,-7/4) -> (7/8,1/1) Hyperbolic Matrix(97,168,56,97) (-7/4,-12/7) -> (12/7,7/4) Hyperbolic Matrix(71,120,-100,-169) (-12/7,-5/3) -> (-5/7,-12/17) Hyperbolic Matrix(73,120,132,217) (-5/3,-18/11) -> (6/11,5/9) Hyperbolic Matrix(265,432,192,313) (-18/11,-13/8) -> (11/8,18/13) Hyperbolic Matrix(119,192,44,71) (-13/8,-8/5) -> (8/3,11/4) Hyperbolic Matrix(121,192,-196,-311) (-8/5,-11/7) -> (-13/21,-8/13) Hyperbolic Matrix(47,72,-32,-49) (-11/7,-3/2) -> (-3/2,-13/9) Parabolic Matrix(599,864,-816,-1177) (-13/9,-36/25) -> (-36/49,-11/15) Hyperbolic Matrix(1201,1728,768,1105) (-36/25,-23/16) -> (25/16,36/23) Hyperbolic Matrix(385,552,-468,-671) (-23/16,-10/7) -> (-14/17,-23/28) Hyperbolic Matrix(169,240,288,409) (-10/7,-17/12) -> (7/12,10/17) Hyperbolic Matrix(577,816,408,577) (-17/12,-24/17) -> (24/17,17/12) Hyperbolic Matrix(409,576,120,169) (-24/17,-7/5) -> (17/5,24/7) Hyperbolic Matrix(121,168,-224,-311) (-7/5,-18/13) -> (-6/11,-7/13) Hyperbolic Matrix(313,432,192,265) (-18/13,-11/8) -> (13/8,18/11) Hyperbolic Matrix(193,264,-280,-383) (-11/8,-15/11) -> (-9/13,-11/16) Hyperbolic Matrix(71,96,88,119) (-15/11,-4/3) -> (4/5,9/11) Hyperbolic Matrix(73,96,92,121) (-4/3,-13/10) -> (11/14,4/5) Hyperbolic Matrix(167,216,92,119) (-13/10,-9/7) -> (9/5,11/6) Hyperbolic Matrix(337,432,188,241) (-9/7,-23/18) -> (25/14,9/5) Hyperbolic Matrix(527,672,-716,-913) (-23/18,-14/11) -> (-14/19,-25/34) Hyperbolic Matrix(455,576,-816,-1033) (-19/15,-24/19) -> (-24/43,-5/9) Hyperbolic Matrix(457,576,96,121) (-24/19,-5/4) -> (19/4,24/5) Hyperbolic Matrix(215,264,136,167) (-5/4,-11/9) -> (11/7,19/12) Hyperbolic Matrix(217,264,60,73) (-11/9,-6/5) -> (18/5,11/3) Hyperbolic Matrix(143,168,40,47) (-6/5,-7/6) -> (7/2,18/5) Hyperbolic Matrix(145,168,208,241) (-7/6,-8/7) -> (16/23,7/10) Hyperbolic Matrix(191,216,84,95) (-8/7,-1/1) -> (25/11,16/7) Hyperbolic Matrix(191,168,108,95) (-1/1,-7/8) -> (7/4,23/13) Hyperbolic Matrix(361,312,140,121) (-7/8,-6/7) -> (18/7,31/12) Hyperbolic Matrix(143,120,56,47) (-6/7,-5/6) -> (5/2,18/7) Hyperbolic Matrix(407,336,-728,-601) (-5/6,-14/17) -> (-14/25,-19/34) Hyperbolic Matrix(263,216,28,23) (-23/28,-9/11) -> (9/1,1/0) Hyperbolic Matrix(119,96,88,71) (-9/11,-4/5) -> (4/3,15/11) Hyperbolic Matrix(121,96,92,73) (-4/5,-11/14) -> (13/10,4/3) Hyperbolic Matrix(311,240,92,71) (-7/9,-10/13) -> (10/3,17/5) Hyperbolic Matrix(95,72,-128,-97) (-10/13,-3/4) -> (-3/4,-14/19) Parabolic Matrix(4343,3192,1664,1223) (-25/34,-36/49) -> (60/23,47/18) Hyperbolic Matrix(265,192,432,313) (-8/11,-13/18) -> (11/18,8/13) Hyperbolic Matrix(167,120,32,23) (-13/18,-5/7) -> (5/1,11/2) Hyperbolic Matrix(409,288,240,169) (-12/17,-7/10) -> (17/10,12/7) Hyperbolic Matrix(241,168,208,145) (-7/10,-16/23) -> (8/7,7/6) Hyperbolic Matrix(1729,1200,1108,769) (-25/36,-9/13) -> (39/25,25/16) Hyperbolic Matrix(71,48,-108,-73) (-11/16,-2/3) -> (-2/3,-13/20) Parabolic Matrix(2255,1464,516,335) (-13/20,-24/37) -> (48/11,35/8) Hyperbolic Matrix(263,168,36,23) (-16/25,-7/11) -> (7/1,8/1) Hyperbolic Matrix(457,288,192,121) (-12/19,-5/8) -> (19/8,12/5) Hyperbolic Matrix(193,120,156,97) (-5/8,-13/21) -> (11/9,5/4) Hyperbolic Matrix(313,192,432,265) (-8/13,-11/18) -> (13/18,8/11) Hyperbolic Matrix(119,72,-200,-121) (-11/18,-3/5) -> (-3/5,-13/22) Parabolic Matrix(4391,2592,1340,791) (-13/22,-36/61) -> (36/11,59/18) Hyperbolic Matrix(1751,1032,772,455) (-23/39,-10/17) -> (34/15,25/11) Hyperbolic Matrix(409,240,288,169) (-10/17,-7/12) -> (17/12,10/7) Hyperbolic Matrix(289,168,332,193) (-7/12,-18/31) -> (6/7,7/8) Hyperbolic Matrix(167,96,40,23) (-11/19,-4/7) -> (4/1,13/3) Hyperbolic Matrix(169,96,44,25) (-4/7,-9/16) -> (15/4,4/1) Hyperbolic Matrix(1199,672,1968,1103) (-23/41,-14/25) -> (14/23,25/41) Hyperbolic Matrix(2063,1152,428,239) (-19/34,-24/43) -> (24/5,29/6) Hyperbolic Matrix(217,120,132,73) (-5/9,-6/11) -> (18/11,5/3) Hyperbolic Matrix(313,168,136,73) (-7/13,-1/2) -> (23/10,7/3) Hyperbolic Matrix(1,0,4,1) (-1/2,0/1) -> (0/1,1/2) Parabolic Matrix(311,-168,224,-121) (1/2,6/11) -> (18/13,25/18) Hyperbolic Matrix(601,-336,728,-407) (5/9,14/25) -> (14/17,19/23) Hyperbolic Matrix(769,-432,340,-191) (14/25,9/16) -> (9/4,34/15) Hyperbolic Matrix(745,-432,288,-167) (11/19,7/12) -> (31/12,13/5) Hyperbolic Matrix(121,-72,200,-119) (10/17,3/5) -> (3/5,14/23) Parabolic Matrix(2833,-1728,864,-527) (25/41,11/18) -> (59/18,23/7) Hyperbolic Matrix(311,-192,196,-121) (8/13,5/8) -> (19/12,8/5) Hyperbolic Matrix(265,-168,112,-71) (5/8,7/11) -> (7/3,19/8) Hyperbolic Matrix(673,-432,148,-95) (16/25,9/14) -> (9/2,32/7) Hyperbolic Matrix(335,-216,76,-49) (9/14,2/3) -> (22/5,9/2) Hyperbolic Matrix(383,-264,280,-193) (2/3,9/13) -> (15/11,26/19) Hyperbolic Matrix(311,-216,36,-25) (9/13,16/23) -> (8/1,9/1) Hyperbolic Matrix(169,-120,100,-71) (7/10,5/7) -> (5/3,17/10) Hyperbolic Matrix(263,-192,100,-73) (8/11,3/4) -> (21/8,8/3) Hyperbolic Matrix(409,-312,156,-119) (3/4,10/13) -> (34/13,21/8) Hyperbolic Matrix(215,-168,32,-25) (7/9,11/14) -> (13/2,7/1) Hyperbolic Matrix(817,-672,524,-431) (9/11,14/17) -> (14/9,39/25) Hyperbolic Matrix(697,-576,144,-119) (19/23,5/6) -> (29/6,5/1) Hyperbolic Matrix(265,-336,56,-71) (5/4,14/11) -> (14/3,19/4) Hyperbolic Matrix(1129,-1440,432,-551) (14/11,23/18) -> (47/18,34/13) Hyperbolic Matrix(841,-1152,192,-263) (26/19,11/8) -> (35/8,22/5) Hyperbolic Matrix(49,-72,32,-47) (10/7,3/2) -> (3/2,14/9) Parabolic Matrix(719,-1128,276,-433) (36/23,11/7) -> (13/5,60/23) Hyperbolic Matrix(623,-1104,136,-241) (23/13,16/9) -> (32/7,23/5) Hyperbolic Matrix(25,-48,12,-23) (11/6,2/1) -> (2/1,13/6) Parabolic Matrix(383,-840,88,-193) (24/11,11/5) -> (13/3,48/11) Hyperbolic Matrix(25,-72,8,-23) (11/4,3/1) -> (3/1,13/4) Parabolic Matrix(25,-144,4,-23) (11/2,6/1) -> (6/1,13/2) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(25,216,-36,-311) -> Matrix(1,0,0,1) Matrix(23,168,36,263) -> Matrix(1,2,-2,-3) Matrix(25,168,-32,-215) -> Matrix(1,4,0,1) Matrix(47,264,-60,-337) -> Matrix(1,4,0,1) Matrix(23,120,32,167) -> Matrix(1,4,-2,-7) Matrix(71,336,-56,-265) -> Matrix(1,0,0,1) Matrix(119,552,36,167) -> Matrix(1,2,2,5) Matrix(95,432,-148,-673) -> Matrix(11,24,-6,-13) Matrix(49,216,-76,-335) -> Matrix(9,16,-4,-7) Matrix(23,96,40,167) -> Matrix(1,2,-2,-3) Matrix(25,96,44,169) -> Matrix(1,2,-4,-7) Matrix(71,264,32,119) -> Matrix(3,4,2,3) Matrix(73,264,60,217) -> Matrix(3,4,-4,-5) Matrix(47,168,40,143) -> Matrix(1,2,-2,-3) Matrix(97,336,28,97) -> Matrix(5,8,-2,-3) Matrix(169,576,120,409) -> Matrix(7,10,-26,-37) Matrix(71,240,92,311) -> Matrix(3,4,-4,-5) Matrix(23,72,-8,-25) -> Matrix(3,4,-4,-5) Matrix(241,672,52,145) -> Matrix(1,0,2,1) Matrix(623,1728,-1056,-2929) -> Matrix(11,2,-6,-1) Matrix(313,864,96,265) -> Matrix(1,0,-2,1) Matrix(71,192,44,119) -> Matrix(1,0,2,1) Matrix(73,192,-100,-263) -> Matrix(1,-4,0,1) Matrix(167,432,-288,-745) -> Matrix(1,0,0,1) Matrix(47,120,56,143) -> Matrix(1,2,-2,-3) Matrix(49,120,20,49) -> Matrix(1,2,-2,-3) Matrix(71,168,-112,-265) -> Matrix(1,0,0,1) Matrix(145,336,104,241) -> Matrix(3,4,-10,-13) Matrix(335,768,188,431) -> Matrix(1,2,0,1) Matrix(95,216,84,191) -> Matrix(1,2,-2,-3) Matrix(191,432,-340,-769) -> Matrix(5,8,-2,-3) Matrix(119,264,32,71) -> Matrix(3,4,-4,-5) Matrix(23,48,-12,-25) -> Matrix(5,6,-6,-7) Matrix(311,576,-480,-889) -> Matrix(7,4,-2,-1) Matrix(313,576,144,265) -> Matrix(3,2,4,3) Matrix(119,216,92,167) -> Matrix(1,0,0,1) Matrix(241,432,188,337) -> Matrix(5,4,-4,-3) Matrix(431,768,188,335) -> Matrix(5,4,-4,-3) Matrix(433,768,-676,-1199) -> Matrix(17,12,-10,-7) Matrix(95,168,108,191) -> Matrix(3,2,-8,-5) Matrix(97,168,56,97) -> Matrix(1,0,2,1) Matrix(71,120,-100,-169) -> Matrix(7,4,-2,-1) Matrix(73,120,132,217) -> Matrix(1,2,-2,-3) Matrix(265,432,192,313) -> Matrix(5,4,-14,-11) Matrix(119,192,44,71) -> Matrix(3,2,-2,-1) Matrix(121,192,-196,-311) -> Matrix(3,2,-2,-1) Matrix(47,72,-32,-49) -> Matrix(1,0,2,1) Matrix(599,864,-816,-1177) -> Matrix(1,-8,0,1) Matrix(1201,1728,768,1105) -> Matrix(1,4,4,17) Matrix(385,552,-468,-671) -> Matrix(1,0,2,1) Matrix(169,240,288,409) -> Matrix(1,-2,0,1) Matrix(577,816,408,577) -> Matrix(1,-4,-4,17) Matrix(409,576,120,169) -> Matrix(1,2,0,1) Matrix(121,168,-224,-311) -> Matrix(1,0,0,1) Matrix(313,432,192,265) -> Matrix(1,0,2,1) Matrix(193,264,-280,-383) -> Matrix(1,-2,0,1) Matrix(71,96,88,119) -> Matrix(1,0,-2,1) Matrix(73,96,92,121) -> Matrix(1,2,-2,-3) Matrix(167,216,92,119) -> Matrix(1,2,0,1) Matrix(337,432,188,241) -> Matrix(1,2,0,1) Matrix(527,672,-716,-913) -> Matrix(1,-4,0,1) Matrix(455,576,-816,-1033) -> Matrix(3,8,-2,-5) Matrix(457,576,96,121) -> Matrix(1,2,-4,-7) Matrix(215,264,136,167) -> Matrix(3,4,8,11) Matrix(217,264,60,73) -> Matrix(5,6,-6,-7) Matrix(143,168,40,47) -> Matrix(5,4,-4,-3) Matrix(145,168,208,241) -> Matrix(1,0,0,1) Matrix(191,216,84,95) -> Matrix(7,4,-2,-1) Matrix(191,168,108,95) -> Matrix(1,0,0,1) Matrix(361,312,140,121) -> Matrix(1,0,0,1) Matrix(143,120,56,47) -> Matrix(1,0,0,1) Matrix(407,336,-728,-601) -> Matrix(5,-2,-2,1) Matrix(263,216,28,23) -> Matrix(3,-2,2,-1) Matrix(119,96,88,71) -> Matrix(1,-2,-2,5) Matrix(121,96,92,73) -> Matrix(1,0,-2,1) Matrix(311,240,92,71) -> Matrix(1,-2,0,1) Matrix(95,72,-128,-97) -> Matrix(1,-10,0,1) Matrix(4343,3192,1664,1223) -> Matrix(1,2,0,1) Matrix(265,192,432,313) -> Matrix(1,6,-2,-11) Matrix(167,120,32,23) -> Matrix(1,4,0,1) Matrix(409,288,240,169) -> Matrix(1,2,2,5) Matrix(241,168,208,145) -> Matrix(1,2,0,1) Matrix(1729,1200,1108,769) -> Matrix(1,4,4,17) Matrix(71,48,-108,-73) -> Matrix(1,0,0,1) Matrix(2255,1464,516,335) -> Matrix(1,2,0,1) Matrix(263,168,36,23) -> Matrix(1,2,-2,-3) Matrix(457,288,192,121) -> Matrix(1,0,0,1) Matrix(193,120,156,97) -> Matrix(1,2,-2,-3) Matrix(313,192,432,265) -> Matrix(1,4,-2,-7) Matrix(119,72,-200,-121) -> Matrix(1,0,0,1) Matrix(4391,2592,1340,791) -> Matrix(1,2,4,9) Matrix(1751,1032,772,455) -> Matrix(9,14,-2,-3) Matrix(409,240,288,169) -> Matrix(1,0,-4,1) Matrix(289,168,332,193) -> Matrix(1,2,-2,-3) Matrix(167,96,40,23) -> Matrix(1,2,0,1) Matrix(169,96,44,25) -> Matrix(1,2,-2,-3) Matrix(1199,672,1968,1103) -> Matrix(3,4,-4,-5) Matrix(2063,1152,428,239) -> Matrix(1,2,6,13) Matrix(217,120,132,73) -> Matrix(1,2,0,1) Matrix(313,168,136,73) -> Matrix(1,0,0,1) Matrix(1,0,4,1) -> Matrix(1,2,-2,-3) Matrix(311,-168,224,-121) -> Matrix(3,4,-10,-13) Matrix(601,-336,728,-407) -> Matrix(3,2,-14,-9) Matrix(769,-432,340,-191) -> Matrix(15,8,-2,-1) Matrix(745,-432,288,-167) -> Matrix(1,0,0,1) Matrix(121,-72,200,-119) -> Matrix(3,4,-4,-5) Matrix(2833,-1728,864,-527) -> Matrix(3,2,10,7) Matrix(311,-192,196,-121) -> Matrix(1,0,4,1) Matrix(265,-168,112,-71) -> Matrix(3,2,-2,-1) Matrix(673,-432,148,-95) -> Matrix(1,0,2,1) Matrix(335,-216,76,-49) -> Matrix(1,0,0,1) Matrix(383,-264,280,-193) -> Matrix(3,2,-8,-5) Matrix(311,-216,36,-25) -> Matrix(3,2,4,3) Matrix(169,-120,100,-71) -> Matrix(3,2,4,3) Matrix(263,-192,100,-73) -> Matrix(3,2,-2,-1) Matrix(409,-312,156,-119) -> Matrix(1,0,2,1) Matrix(215,-168,32,-25) -> Matrix(1,0,2,1) Matrix(817,-672,524,-431) -> Matrix(5,2,22,9) Matrix(697,-576,144,-119) -> Matrix(1,0,6,1) Matrix(265,-336,56,-71) -> Matrix(1,0,0,1) Matrix(1129,-1440,432,-551) -> Matrix(1,0,0,1) Matrix(841,-1152,192,-263) -> Matrix(1,0,2,1) Matrix(49,-72,32,-47) -> Matrix(1,0,10,1) Matrix(719,-1128,276,-433) -> Matrix(7,-2,4,-1) Matrix(623,-1104,136,-241) -> Matrix(1,0,0,1) Matrix(25,-48,12,-23) -> Matrix(1,0,0,1) Matrix(383,-840,88,-193) -> Matrix(1,-2,0,1) Matrix(25,-72,8,-23) -> Matrix(1,0,0,1) Matrix(25,-144,4,-23) -> 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): 32 Degree of the the map X: 32 Degree of the the map Y: 128 ----------------------------------------------------------------------- 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): 384 Minimal number of generators: 65 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: 40 Genus: 13 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -6/1 -5/1 -4/1 -10/3 -3/1 -8/3 -2/1 -18/11 -3/2 -10/7 -6/5 -1/1 -6/7 -3/4 -2/3 -3/5 -6/11 0/1 1/2 3/5 2/3 6/7 1/1 6/5 10/7 3/2 2/1 12/5 5/2 8/3 3/1 36/11 10/3 24/7 7/2 4/1 9/2 5/1 6/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -6/1 -3/1 -1/1 -11/2 -2/1 -5/1 -3/1 -2/1 1/0 -4/1 -2/1 -7/2 -2/1 -24/7 -3/2 -17/5 -3/2 -7/5 -4/3 -10/3 -7/5 -1/1 -3/1 -1/1 -14/5 -1/1 -1/3 -25/9 -1/2 -1/3 0/1 -36/13 0/1 -11/4 1/0 -8/3 1/0 -13/5 -3/1 -2/1 1/0 -18/7 -3/1 -1/1 -5/2 -2/1 -2/1 -1/1 -7/4 -1/2 -12/7 -1/1 -5/3 -1/1 -1/2 0/1 -18/11 -1/1 -13/8 -3/4 -8/5 -1/2 -11/7 -1/1 -2/3 -1/2 -3/2 0/1 -13/9 1/1 2/1 1/0 -36/25 1/0 -23/16 1/0 -10/7 -1/1 1/1 -17/12 1/0 -24/17 1/0 -7/5 -2/1 -1/1 1/0 -4/3 1/0 -5/4 -3/2 -6/5 -1/1 -7/6 -2/3 -1/1 -1/1 0/1 1/0 -6/7 -1/1 1/1 -5/6 0/1 -4/5 1/0 -7/9 2/1 3/1 1/0 -10/13 3/1 -3/4 1/0 -14/19 -7/1 -11/15 -7/1 -6/1 1/0 -8/11 1/0 -13/18 -4/1 -5/7 -4/1 -3/1 1/0 -2/3 -3/1 -1/1 -7/11 -2/1 -3/2 -1/1 -12/19 -1/1 -5/8 1/0 -13/21 -1/1 0/1 1/0 -8/13 1/0 -11/18 -2/1 -3/5 -3/1 -1/1 -13/22 -2/1 -10/17 -1/1 -7/12 1/0 -4/7 -2/1 -5/9 -2/1 -3/2 -1/1 -6/11 -1/1 -1/2 -2/1 0/1 -1/1 1/2 0/1 4/7 0/1 7/12 1/0 10/17 -3/1 -1/1 3/5 -1/1 14/23 -1/1 -5/7 11/18 -2/3 8/13 -1/2 5/8 -1/2 2/3 -1/1 7/10 -2/3 5/7 -1/1 -2/3 -1/2 13/18 -2/3 8/11 -1/2 3/4 -1/2 4/5 -1/2 5/6 0/1 6/7 -1/1 -1/3 1/1 -1/1 -1/2 0/1 6/5 -1/1 11/9 -1/1 -2/3 -1/2 5/4 -1/2 4/3 -1/2 11/8 -1/2 18/13 -1/3 7/5 -1/3 -2/7 -1/4 24/17 -1/4 17/12 -1/4 10/7 -1/5 3/2 0/1 14/9 1/5 25/16 1/4 36/23 1/4 11/7 1/4 2/7 1/3 19/12 1/2 8/5 1/2 13/8 1/2 18/11 1/1 5/3 0/1 1/2 1/1 2/1 -1/1 1/1 7/3 -2/1 -1/1 1/0 19/8 1/0 12/5 -1/1 5/2 0/1 18/7 -1/1 1/1 13/5 0/1 1/1 1/0 21/8 1/0 8/3 1/0 11/4 -1/2 3/1 -1/1 1/1 13/4 -1/2 36/11 0/1 23/7 0/1 1/1 1/0 10/3 1/1 17/5 0/1 1/1 1/0 24/7 1/0 7/2 -2/1 4/1 0/1 9/2 0/1 23/5 -1/1 0/1 1/0 14/3 -1/1 1/1 5/1 0/1 1/1 1/0 6/1 -1/1 1/1 7/1 -1/1 0/1 1/0 1/0 1/0 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(11,72,-2,-13) (-6/1,1/0) -> (-6/1,-11/2) Parabolic Matrix(23,120,32,167) (-11/2,-5/1) -> (5/7,13/18) Hyperbolic Matrix(11,48,-14,-61) (-5/1,-4/1) -> (-4/5,-7/9) Hyperbolic Matrix(13,48,10,37) (-4/1,-7/2) -> (5/4,4/3) Hyperbolic Matrix(97,336,28,97) (-7/2,-24/7) -> (24/7,7/2) Hyperbolic Matrix(169,576,120,409) (-24/7,-17/5) -> (7/5,24/17) Hyperbolic Matrix(85,288,18,61) (-17/5,-10/3) -> (14/3,5/1) Hyperbolic Matrix(23,72,-8,-25) (-10/3,-3/1) -> (-3/1,-14/5) Parabolic Matrix(241,672,52,145) (-14/5,-25/9) -> (23/5,14/3) Hyperbolic Matrix(467,1296,298,827) (-25/9,-36/13) -> (36/23,11/7) Hyperbolic Matrix(313,864,96,265) (-36/13,-11/4) -> (13/4,36/11) Hyperbolic Matrix(71,192,44,119) (-11/4,-8/3) -> (8/5,13/8) Hyperbolic Matrix(73,192,-100,-263) (-8/3,-13/5) -> (-11/15,-8/11) Hyperbolic Matrix(37,96,42,109) (-13/5,-18/7) -> (6/7,1/1) Hyperbolic Matrix(47,120,56,143) (-18/7,-5/2) -> (5/6,6/7) Hyperbolic Matrix(11,24,-6,-13) (-5/2,-2/1) -> (-2/1,-7/4) Parabolic Matrix(83,144,34,59) (-7/4,-12/7) -> (12/5,5/2) Hyperbolic Matrix(85,144,-134,-227) (-12/7,-5/3) -> (-7/11,-12/19) Hyperbolic Matrix(131,216,94,155) (-5/3,-18/11) -> (18/13,7/5) Hyperbolic Matrix(265,432,192,313) (-18/11,-13/8) -> (11/8,18/13) Hyperbolic Matrix(119,192,44,71) (-13/8,-8/5) -> (8/3,11/4) Hyperbolic Matrix(121,192,-196,-311) (-8/5,-11/7) -> (-13/21,-8/13) Hyperbolic Matrix(47,72,-32,-49) (-11/7,-3/2) -> (-3/2,-13/9) Parabolic Matrix(899,1296,274,395) (-13/9,-36/25) -> (36/11,23/7) Hyperbolic Matrix(1201,1728,768,1105) (-36/25,-23/16) -> (25/16,36/23) Hyperbolic Matrix(301,432,494,709) (-23/16,-10/7) -> (14/23,11/18) Hyperbolic Matrix(169,240,288,409) (-10/7,-17/12) -> (7/12,10/17) Hyperbolic Matrix(577,816,408,577) (-17/12,-24/17) -> (24/17,17/12) Hyperbolic Matrix(409,576,120,169) (-24/17,-7/5) -> (17/5,24/7) Hyperbolic Matrix(35,48,-62,-85) (-7/5,-4/3) -> (-4/7,-5/9) Hyperbolic Matrix(37,48,10,13) (-4/3,-5/4) -> (7/2,4/1) Hyperbolic Matrix(59,72,-50,-61) (-5/4,-6/5) -> (-6/5,-7/6) Parabolic Matrix(85,96,54,61) (-7/6,-1/1) -> (11/7,19/12) Hyperbolic Matrix(109,96,42,37) (-1/1,-6/7) -> (18/7,13/5) Hyperbolic Matrix(143,120,56,47) (-6/7,-5/6) -> (5/2,18/7) Hyperbolic Matrix(59,48,102,83) (-5/6,-4/5) -> (4/7,7/12) Hyperbolic Matrix(311,240,92,71) (-7/9,-10/13) -> (10/3,17/5) Hyperbolic Matrix(95,72,-128,-97) (-10/13,-3/4) -> (-3/4,-14/19) Parabolic Matrix(587,432,178,131) (-14/19,-11/15) -> (23/7,10/3) Hyperbolic Matrix(265,192,432,313) (-8/11,-13/18) -> (11/18,8/13) Hyperbolic Matrix(133,96,18,13) (-13/18,-5/7) -> (7/1,1/0) Hyperbolic Matrix(35,24,-54,-37) (-5/7,-2/3) -> (-2/3,-7/11) Parabolic Matrix(457,288,192,121) (-12/19,-5/8) -> (19/8,12/5) Hyperbolic Matrix(193,120,156,97) (-5/8,-13/21) -> (11/9,5/4) Hyperbolic Matrix(313,192,432,265) (-8/13,-11/18) -> (13/18,8/11) Hyperbolic Matrix(119,72,-200,-121) (-11/18,-3/5) -> (-3/5,-13/22) Parabolic Matrix(733,432,470,277) (-13/22,-10/17) -> (14/9,25/16) Hyperbolic Matrix(409,240,288,169) (-10/17,-7/12) -> (17/12,10/7) Hyperbolic Matrix(83,48,102,59) (-7/12,-4/7) -> (4/5,5/6) Hyperbolic Matrix(217,120,132,73) (-5/9,-6/11) -> (18/11,5/3) Hyperbolic Matrix(179,96,110,59) (-6/11,-1/2) -> (13/8,18/11) Hyperbolic Matrix(1,0,4,1) (-1/2,0/1) -> (0/1,1/2) Parabolic Matrix(85,-48,62,-35) (1/2,4/7) -> (4/3,11/8) Hyperbolic Matrix(121,-72,200,-119) (10/17,3/5) -> (3/5,14/23) Parabolic Matrix(311,-192,196,-121) (8/13,5/8) -> (19/12,8/5) Hyperbolic Matrix(37,-24,54,-35) (5/8,2/3) -> (2/3,7/10) Parabolic Matrix(203,-144,86,-61) (7/10,5/7) -> (7/3,19/8) Hyperbolic Matrix(263,-192,100,-73) (8/11,3/4) -> (21/8,8/3) Hyperbolic Matrix(61,-48,14,-11) (3/4,4/5) -> (4/1,9/2) Hyperbolic Matrix(61,-72,50,-59) (1/1,6/5) -> (6/5,11/9) Parabolic Matrix(49,-72,32,-47) (10/7,3/2) -> (3/2,14/9) Parabolic Matrix(13,-24,6,-11) (5/3,2/1) -> (2/1,7/3) Parabolic Matrix(229,-600,50,-131) (13/5,21/8) -> (9/2,23/5) Hyperbolic Matrix(25,-72,8,-23) (11/4,3/1) -> (3/1,13/4) Parabolic Matrix(13,-72,2,-11) (5/1,6/1) -> (6/1,7/1) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(11,72,-2,-13) -> Matrix(2,5,-1,-2) Matrix(23,120,32,167) -> Matrix(1,4,-2,-7) Matrix(11,48,-14,-61) -> Matrix(2,3,1,2) Matrix(13,48,10,37) -> Matrix(2,3,-3,-4) Matrix(97,336,28,97) -> Matrix(5,8,-2,-3) Matrix(169,576,120,409) -> Matrix(7,10,-26,-37) Matrix(85,288,18,61) -> Matrix(2,3,-3,-4) Matrix(23,72,-8,-25) -> Matrix(3,4,-4,-5) Matrix(241,672,52,145) -> Matrix(1,0,2,1) Matrix(467,1296,298,827) -> Matrix(4,1,15,4) Matrix(313,864,96,265) -> Matrix(1,0,-2,1) Matrix(71,192,44,119) -> Matrix(1,0,2,1) Matrix(73,192,-100,-263) -> Matrix(1,-4,0,1) Matrix(37,96,42,109) -> Matrix(0,-1,1,4) Matrix(47,120,56,143) -> Matrix(1,2,-2,-3) Matrix(11,24,-6,-13) -> Matrix(2,3,-3,-4) Matrix(83,144,34,59) -> Matrix(2,1,-1,0) Matrix(85,144,-134,-227) -> Matrix(4,3,-3,-2) Matrix(131,216,94,155) -> Matrix(0,-1,1,4) Matrix(265,432,192,313) -> Matrix(5,4,-14,-11) Matrix(119,192,44,71) -> Matrix(3,2,-2,-1) Matrix(121,192,-196,-311) -> Matrix(3,2,-2,-1) Matrix(47,72,-32,-49) -> Matrix(1,0,2,1) Matrix(899,1296,274,395) -> Matrix(0,1,-1,2) Matrix(1201,1728,768,1105) -> Matrix(1,4,4,17) Matrix(301,432,494,709) -> Matrix(2,3,-3,-4) Matrix(169,240,288,409) -> Matrix(1,-2,0,1) Matrix(577,816,408,577) -> Matrix(1,-4,-4,17) Matrix(409,576,120,169) -> Matrix(1,2,0,1) Matrix(35,48,-62,-85) -> Matrix(2,1,-1,0) Matrix(37,48,10,13) -> Matrix(0,-1,1,2) Matrix(59,72,-50,-61) -> Matrix(4,5,-5,-6) Matrix(85,96,54,61) -> Matrix(2,1,7,4) Matrix(109,96,42,37) -> Matrix(0,-1,1,0) Matrix(143,120,56,47) -> Matrix(1,0,0,1) Matrix(59,48,102,83) -> Matrix(0,-1,1,0) Matrix(311,240,92,71) -> Matrix(1,-2,0,1) Matrix(95,72,-128,-97) -> Matrix(1,-10,0,1) Matrix(587,432,178,131) -> Matrix(0,-1,1,6) Matrix(265,192,432,313) -> Matrix(1,6,-2,-11) Matrix(133,96,18,13) -> Matrix(0,-1,1,4) Matrix(35,24,-54,-37) -> Matrix(2,5,-1,-2) Matrix(457,288,192,121) -> Matrix(1,0,0,1) Matrix(193,120,156,97) -> Matrix(1,2,-2,-3) Matrix(313,192,432,265) -> Matrix(1,4,-2,-7) Matrix(119,72,-200,-121) -> Matrix(1,0,0,1) Matrix(733,432,470,277) -> Matrix(2,3,9,14) Matrix(409,240,288,169) -> Matrix(1,0,-4,1) Matrix(83,48,102,59) -> Matrix(0,-1,1,4) Matrix(217,120,132,73) -> Matrix(1,2,0,1) Matrix(179,96,110,59) -> Matrix(0,-1,1,0) Matrix(1,0,4,1) -> Matrix(1,2,-2,-3) Matrix(85,-48,62,-35) -> Matrix(2,1,-5,-2) Matrix(121,-72,200,-119) -> Matrix(3,4,-4,-5) Matrix(311,-192,196,-121) -> Matrix(1,0,4,1) Matrix(37,-24,54,-35) -> Matrix(0,-1,1,2) Matrix(203,-144,86,-61) -> Matrix(4,3,-3,-2) Matrix(263,-192,100,-73) -> Matrix(3,2,-2,-1) Matrix(61,-48,14,-11) -> Matrix(2,1,-1,0) Matrix(61,-72,50,-59) -> Matrix(0,-1,1,2) Matrix(49,-72,32,-47) -> Matrix(1,0,10,1) Matrix(13,-24,6,-11) -> Matrix(0,-1,1,0) Matrix(229,-600,50,-131) -> Matrix(0,-1,1,0) Matrix(25,-72,8,-23) -> Matrix(1,0,0,1) Matrix(13,-72,2,-11) -> Matrix(0,-1,1,0) 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): 32 ----------------------------------------------------------------------- INFORMATION ON THE IMAGE IN PGL(2,Z) OF THE GROUP OF EXTENDED MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE c d -6/1 (-3/1,-1/1).(-2/1,1/0) 0 2 -5/1 0 12 -4/1 -2/1 1 6 -7/2 -2/1 1 12 -24/7 -3/2 6 2 -17/5 0 12 -10/3 (-3/2,-4/3).(-7/5,-1/1) 0 6 -3/1 -1/1 2 4 -2/1 -1/1 3 6 -3/2 0/1 1 4 -10/7 (-1/1,1/1).(0/1,1/0) 0 6 -17/12 1/0 1 12 -24/17 1/0 6 2 -7/5 0 12 -4/3 1/0 1 6 -5/4 -3/2 1 12 -6/5 -1/1 5 2 -1/1 0 12 -5/6 0/1 1 12 -4/5 1/0 1 6 -7/9 0 12 -10/13 3/1 1 6 -3/4 1/0 5 4 -2/3 (-3/1,-1/1).(-2/1,1/0) 0 6 -3/5 (-3/1,-1/1) 0 4 -10/17 -1/1 3 6 -7/12 1/0 1 12 -4/7 -2/1 1 6 -5/9 0 12 -1/2 -2/1 1 12 0/1 -1/1 1 2 1/2 0/1 1 12 4/7 0/1 1 6 7/12 1/0 1 12 10/17 (-3/1,-1/1).(-2/1,1/0) 0 6 3/5 -1/1 2 4 2/3 -1/1 1 6 3/4 -1/2 1 4 4/5 -1/2 1 6 5/6 0/1 1 12 6/7 (-1/1,-1/3).(-1/2,0/1) 0 2 1/1 0 12 6/5 -1/1 1 2 11/9 0 12 5/4 -1/2 1 12 4/3 -1/2 1 6 11/8 -1/2 1 12 18/13 -1/3 5 2 7/5 0 12 24/17 -1/4 6 2 17/12 -1/4 1 12 10/7 -1/5 3 6 3/2 0/1 5 4 2/1 (-1/1,1/1).(0/1,1/0) 0 6 3/1 (-1/1,1/1) 0 4 10/3 1/1 1 6 17/5 0 12 24/7 1/0 6 2 7/2 -2/1 1 12 4/1 0/1 1 6 9/2 0/1 1 4 14/3 (-1/1,1/1).(0/1,1/0) 0 6 5/1 0 12 6/1 (-1/1,1/1).(0/1,1/0) 0 2 7/1 0 12 1/0 1/0 1 12 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(5,36,6,43) (-6/1,1/0) -> (5/6,6/7) Glide Reflection Matrix(7,36,8,41) (-6/1,-5/1) -> (6/7,1/1) Glide Reflection Matrix(11,48,-14,-61) (-5/1,-4/1) -> (-4/5,-7/9) Hyperbolic Matrix(13,48,10,37) (-4/1,-7/2) -> (5/4,4/3) Hyperbolic Matrix(97,336,28,97) (-7/2,-24/7) -> (24/7,7/2) Hyperbolic Matrix(169,576,120,409) (-24/7,-17/5) -> (7/5,24/17) Hyperbolic Matrix(85,288,18,61) (-17/5,-10/3) -> (14/3,5/1) Hyperbolic Matrix(19,60,-6,-19) (-10/3,-3/1) -> (-10/3,-3/1) Reflection Matrix(5,12,-2,-5) (-3/1,-2/1) -> (-3/1,-2/1) Reflection Matrix(7,12,-4,-7) (-2/1,-3/2) -> (-2/1,-3/2) Reflection Matrix(41,60,-28,-41) (-3/2,-10/7) -> (-3/2,-10/7) Reflection Matrix(169,240,288,409) (-10/7,-17/12) -> (7/12,10/17) Hyperbolic Matrix(577,816,408,577) (-17/12,-24/17) -> (24/17,17/12) Hyperbolic Matrix(409,576,120,169) (-24/17,-7/5) -> (17/5,24/7) Hyperbolic Matrix(35,48,-62,-85) (-7/5,-4/3) -> (-4/7,-5/9) Hyperbolic Matrix(37,48,10,13) (-4/3,-5/4) -> (7/2,4/1) Hyperbolic Matrix(127,156,92,113) (-5/4,-6/5) -> (11/8,18/13) Glide Reflection Matrix(53,60,38,43) (-6/5,-1/1) -> (18/13,7/5) Glide Reflection Matrix(43,36,6,5) (-1/1,-5/6) -> (7/1,1/0) Glide Reflection Matrix(59,48,102,83) (-5/6,-4/5) -> (4/7,7/12) Hyperbolic Matrix(311,240,92,71) (-7/9,-10/13) -> (10/3,17/5) Hyperbolic Matrix(79,60,-104,-79) (-10/13,-3/4) -> (-10/13,-3/4) Reflection Matrix(17,12,-24,-17) (-3/4,-2/3) -> (-3/4,-2/3) Reflection Matrix(19,12,-30,-19) (-2/3,-3/5) -> (-2/3,-3/5) Reflection Matrix(101,60,-170,-101) (-3/5,-10/17) -> (-3/5,-10/17) Reflection Matrix(409,240,288,169) (-10/17,-7/12) -> (17/12,10/7) Hyperbolic Matrix(83,48,102,59) (-7/12,-4/7) -> (4/5,5/6) Hyperbolic Matrix(67,36,54,29) (-5/9,-1/2) -> (11/9,5/4) Glide Reflection Matrix(1,0,4,1) (-1/2,0/1) -> (0/1,1/2) Parabolic Matrix(85,-48,62,-35) (1/2,4/7) -> (4/3,11/8) Hyperbolic Matrix(101,-60,170,-101) (10/17,3/5) -> (10/17,3/5) Reflection Matrix(19,-12,30,-19) (3/5,2/3) -> (3/5,2/3) Reflection Matrix(17,-12,24,-17) (2/3,3/4) -> (2/3,3/4) Reflection Matrix(61,-48,14,-11) (3/4,4/5) -> (4/1,9/2) Hyperbolic Matrix(61,-72,50,-59) (1/1,6/5) -> (6/5,11/9) Parabolic Matrix(41,-60,28,-41) (10/7,3/2) -> (10/7,3/2) Reflection Matrix(7,-12,4,-7) (3/2,2/1) -> (3/2,2/1) Reflection Matrix(5,-12,2,-5) (2/1,3/1) -> (2/1,3/1) Reflection Matrix(19,-60,6,-19) (3/1,10/3) -> (3/1,10/3) Reflection Matrix(55,-252,12,-55) (9/2,14/3) -> (9/2,14/3) Reflection Matrix(13,-72,2,-11) (5/1,6/1) -> (6/1,7/1) Parabolic IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(5,36,6,43) -> Matrix(0,1,1,0) *** -> (-1/1,1/1) Matrix(7,36,8,41) -> Matrix(1,2,-2,-5) Matrix(11,48,-14,-61) -> Matrix(2,3,1,2) Matrix(13,48,10,37) -> Matrix(2,3,-3,-4) -1/1 Matrix(97,336,28,97) -> Matrix(5,8,-2,-3) -2/1 Matrix(169,576,120,409) -> Matrix(7,10,-26,-37) Matrix(85,288,18,61) -> Matrix(2,3,-3,-4) -1/1 Matrix(19,60,-6,-19) -> Matrix(6,7,-5,-6) (-10/3,-3/1) -> (-7/5,-1/1) Matrix(5,12,-2,-5) -> Matrix(2,3,-1,-2) (-3/1,-2/1) -> (-3/1,-1/1) Matrix(7,12,-4,-7) -> Matrix(-1,0,2,1) (-2/1,-3/2) -> (-1/1,0/1) Matrix(41,60,-28,-41) -> Matrix(1,0,0,-1) (-3/2,-10/7) -> (0/1,1/0) Matrix(169,240,288,409) -> Matrix(1,-2,0,1) 1/0 Matrix(577,816,408,577) -> Matrix(1,-4,-4,17) Matrix(409,576,120,169) -> Matrix(1,2,0,1) 1/0 Matrix(35,48,-62,-85) -> Matrix(2,1,-1,0) -1/1 Matrix(37,48,10,13) -> Matrix(0,-1,1,2) -1/1 Matrix(127,156,92,113) -> Matrix(3,4,-8,-11) Matrix(53,60,38,43) -> Matrix(2,1,-7,-4) Matrix(43,36,6,5) -> Matrix(0,1,1,0) *** -> (-1/1,1/1) Matrix(59,48,102,83) -> Matrix(0,-1,1,0) (-1/1,1/1).(0/1,1/0) Matrix(311,240,92,71) -> Matrix(1,-2,0,1) 1/0 Matrix(79,60,-104,-79) -> Matrix(-1,6,0,1) (-10/13,-3/4) -> (3/1,1/0) Matrix(17,12,-24,-17) -> Matrix(1,4,0,-1) (-3/4,-2/3) -> (-2/1,1/0) Matrix(19,12,-30,-19) -> Matrix(2,3,-1,-2) (-2/3,-3/5) -> (-3/1,-1/1) Matrix(101,60,-170,-101) -> Matrix(2,3,-1,-2) (-3/5,-10/17) -> (-3/1,-1/1) Matrix(409,240,288,169) -> Matrix(1,0,-4,1) 0/1 Matrix(83,48,102,59) -> Matrix(0,-1,1,4) Matrix(67,36,54,29) -> Matrix(0,1,1,0) *** -> (-1/1,1/1) Matrix(1,0,4,1) -> Matrix(1,2,-2,-3) -1/1 Matrix(85,-48,62,-35) -> Matrix(2,1,-5,-2) (-1/1,-1/3).(-1/2,0/1) Matrix(101,-60,170,-101) -> Matrix(2,3,-1,-2) (10/17,3/5) -> (-3/1,-1/1) Matrix(19,-12,30,-19) -> Matrix(2,1,-3,-2) (3/5,2/3) -> (-1/1,-1/3) Matrix(17,-12,24,-17) -> Matrix(3,2,-4,-3) (2/3,3/4) -> (-1/1,-1/2) Matrix(61,-48,14,-11) -> Matrix(2,1,-1,0) -1/1 Matrix(61,-72,50,-59) -> Matrix(0,-1,1,2) -1/1 Matrix(41,-60,28,-41) -> Matrix(-1,0,10,1) (10/7,3/2) -> (-1/5,0/1) Matrix(7,-12,4,-7) -> Matrix(1,0,0,-1) (3/2,2/1) -> (0/1,1/0) Matrix(5,-12,2,-5) -> Matrix(0,1,1,0) (2/1,3/1) -> (-1/1,1/1) Matrix(19,-60,6,-19) -> Matrix(0,1,1,0) (3/1,10/3) -> (-1/1,1/1) Matrix(55,-252,12,-55) -> Matrix(1,0,0,-1) (9/2,14/3) -> (0/1,1/0) Matrix(13,-72,2,-11) -> Matrix(0,-1,1,0) (-1/1,1/1).(0/1,1/0) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.