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 -1/2 1/0 -7/1 0/1 1/1 1/0 -6/1 1/0 -11/2 -3/2 1/0 -5/1 -2/1 -1/1 1/0 -14/3 -1/1 1/0 -23/5 -1/1 0/1 1/0 -9/2 -1/1 -13/3 -2/3 -3/5 -1/2 -4/1 -1/2 1/0 -15/4 -1/2 -11/3 -1/1 0/1 1/0 -18/5 -1/2 1/0 -7/2 -1/2 1/0 -24/7 -1/1 -17/5 -1/1 -2/3 -1/2 -10/3 -1/2 -3/1 0/1 -14/5 1/2 -25/9 3/4 4/5 1/1 -36/13 1/1 -11/4 1/0 -8/3 1/0 -13/5 -1/1 0/1 1/0 -18/7 1/0 -5/2 -1/2 1/0 -12/5 0/1 -7/3 0/1 1/2 1/1 -23/10 1/2 1/0 -16/7 1/2 1/0 -25/11 0/1 1/2 1/1 -9/4 1/0 -11/5 -1/1 -1/2 0/1 -2/1 0/1 1/0 -13/7 -1/1 -1/2 0/1 -24/13 0/1 -11/6 1/2 1/0 -9/5 0/1 -25/14 1/2 1/0 -16/9 1/2 1/0 -23/13 1/1 2/1 1/0 -7/4 1/0 -12/7 0/1 -5/3 -1/1 0/1 1/0 -18/11 -1/2 1/0 -13/8 1/0 -8/5 -1/2 -11/7 -1/2 -1/3 0/1 -3/2 0/1 -13/9 0/1 1/6 1/5 -36/25 1/5 -23/16 1/4 -10/7 1/4 -17/12 1/4 -24/17 1/3 -7/5 0/1 1/3 1/2 -18/13 1/4 1/2 -11/8 1/2 -15/11 1/3 -4/3 1/2 -13/10 1/2 5/8 -9/7 1/1 -23/18 1/2 1/0 -14/11 1/2 1/1 -19/15 1/2 2/3 1/1 -24/19 1/1 -5/4 1/0 -11/9 0/1 1/1 1/0 -6/5 1/2 1/0 -7/6 1/2 1/0 -8/7 1/2 1/0 -1/1 0/1 1/1 1/0 -7/8 1/0 -6/7 1/0 -5/6 -3/2 1/0 -14/17 -1/2 -23/28 -1/2 -9/11 0/1 -4/5 1/0 -11/14 1/2 1/0 -18/23 1/0 -7/9 0/1 1/1 1/0 -10/13 1/1 1/0 -3/4 1/0 -14/19 -1/1 1/0 -25/34 -1/2 1/0 -36/49 -1/1 -11/15 -1/1 0/1 1/0 -8/11 1/0 -13/18 3/2 1/0 -5/7 -1/1 0/1 1/0 -12/17 0/1 -7/10 1/2 1/0 -16/23 1/2 1/0 -25/36 1/2 -9/13 1/1 -11/16 3/2 -2/3 1/0 -13/20 -9/2 -24/37 -4/1 -11/17 -4/1 -11/3 -7/2 -9/14 -3/1 -25/39 -3/1 -14/5 -11/4 -16/25 -11/4 -5/2 -7/11 -5/2 -7/3 -2/1 -12/19 -2/1 -5/8 -3/2 -13/21 -2/1 -3/2 -1/1 -8/13 -3/2 -11/18 -3/2 -5/4 -3/5 -1/1 -13/22 -1/2 1/0 -36/61 -1/1 -23/39 -1/1 -3/4 -2/3 -10/17 -1/1 -1/2 -7/12 -1/2 -18/31 -1/2 -11/19 -1/2 -1/3 0/1 -4/7 -1/2 1/0 -9/16 1/0 -23/41 -2/1 -3/2 -1/1 -14/25 1/0 -19/34 -3/2 -5/4 -24/43 -1/1 -5/9 -1/1 -1/2 0/1 -6/11 -1/2 1/0 -7/13 -1/1 -1/2 0/1 -1/2 -1/2 1/0 0/1 0/1 1/2 1/2 1/0 6/11 1/2 1/0 5/9 0/1 1/2 1/1 14/25 1/1 1/0 9/16 1/0 4/7 1/2 1/0 11/19 2/1 3/1 1/0 7/12 1/0 10/17 1/0 3/5 0/1 14/23 1/4 25/41 2/7 3/10 1/3 11/18 3/8 1/2 8/13 1/2 5/8 1/0 7/11 0/1 1/3 1/2 16/25 1/2 1/0 9/14 0/1 2/3 0/1 1/2 9/13 0/1 16/23 1/4 1/2 7/10 1/4 1/2 5/7 0/1 1/3 1/2 13/18 1/4 1/2 8/11 1/2 3/4 1/2 10/13 1/2 7/9 0/1 1/2 1/1 11/14 1/2 5/8 4/5 1/2 9/11 1/1 14/17 1/2 1/1 19/23 2/3 3/4 1/1 5/6 1/2 1/0 6/7 1/2 7/8 1/2 1/1 0/1 1/2 1/1 8/7 1/2 1/0 7/6 1/2 1/0 6/5 1/2 1/0 11/9 0/1 1/2 1/1 5/4 1/2 14/11 1/0 23/18 -1/2 1/0 9/7 0/1 13/10 1/4 1/2 4/3 1/2 15/11 2/3 26/19 1/2 2/3 11/8 3/4 18/13 1/2 3/4 25/18 1/2 3/4 7/5 2/3 3/4 1/1 24/17 1/1 17/12 3/4 10/7 3/4 1/1 3/2 1/1 14/9 1/1 5/4 39/25 1/1 25/16 5/4 36/23 1/1 11/7 1/1 5/4 4/3 19/12 5/4 8/5 3/2 13/8 3/2 18/11 3/2 1/0 5/3 1/1 3/2 2/1 17/10 3/2 1/0 12/7 2/1 7/4 1/0 23/13 -2/1 -1/1 1/0 16/9 1/2 1/0 25/14 1/2 1/0 9/5 1/1 11/6 3/2 7/4 2/1 1/0 13/6 -1/2 -1/4 24/11 0/1 11/5 0/1 1/2 1/1 9/4 1/0 34/15 -1/1 1/0 25/11 -1/1 -1/2 0/1 16/7 -1/2 1/0 23/10 -1/2 1/0 7/3 -1/1 -1/2 0/1 19/8 -1/4 12/5 0/1 5/2 1/4 1/2 18/7 1/2 31/12 1/2 13/5 1/2 2/3 1/1 60/23 1/1 47/18 1/2 1/0 34/13 1/2 21/8 1/2 8/3 1/2 11/4 3/4 3/1 1/1 13/4 1/0 36/11 1/1 59/18 9/8 7/6 23/7 1/1 4/3 3/2 10/3 1/1 3/2 17/5 1/1 3/2 2/1 24/7 1/1 7/2 3/2 1/0 18/5 3/2 1/0 11/3 1/1 3/2 2/1 15/4 1/0 4/1 3/2 1/0 13/3 3/2 5/3 2/1 48/11 2/1 35/8 1/0 22/5 3/2 2/1 9/2 2/1 32/7 13/6 9/4 23/5 9/4 16/7 7/3 14/3 5/2 19/4 11/4 24/5 3/1 29/6 13/4 7/2 5/1 3/1 4/1 1/0 11/2 11/2 1/0 6/1 1/0 13/2 -9/2 1/0 7/1 -3/1 -2/1 1/0 8/1 -1/2 1/0 9/1 0/1 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(1,0,2,1) Matrix(23,168,36,263) -> Matrix(1,0,2,1) Matrix(25,168,-32,-215) -> Matrix(1,0,0,1) Matrix(47,264,-60,-337) -> Matrix(1,2,0,1) Matrix(23,120,32,167) -> Matrix(1,2,2,5) Matrix(71,336,-56,-265) -> Matrix(1,0,2,1) Matrix(119,552,36,167) -> Matrix(3,4,2,3) Matrix(95,432,-148,-673) -> Matrix(11,14,-4,-5) Matrix(49,216,-76,-335) -> Matrix(13,10,-4,-3) Matrix(23,96,40,167) -> Matrix(1,0,2,1) Matrix(25,96,44,169) -> Matrix(1,0,2,1) Matrix(71,264,32,119) -> Matrix(1,0,2,1) Matrix(73,264,60,217) -> Matrix(1,0,2,1) Matrix(47,168,40,143) -> Matrix(1,0,2,1) Matrix(97,336,28,97) -> Matrix(1,2,0,1) Matrix(169,576,120,409) -> Matrix(5,4,6,5) Matrix(71,240,92,311) -> Matrix(3,2,4,3) Matrix(23,72,-8,-25) -> Matrix(1,0,4,1) Matrix(241,672,52,145) -> Matrix(19,-12,8,-5) Matrix(623,1728,-1056,-2929) -> Matrix(7,-6,-8,7) Matrix(313,864,96,265) -> Matrix(1,0,0,1) Matrix(71,192,44,119) -> Matrix(3,-2,2,-1) Matrix(73,192,-100,-263) -> Matrix(1,0,0,1) Matrix(167,432,-288,-745) -> Matrix(1,0,-2,1) Matrix(47,120,56,143) -> Matrix(1,0,2,1) Matrix(49,120,20,49) -> Matrix(1,0,4,1) Matrix(71,168,-112,-265) -> Matrix(9,-2,-4,1) Matrix(145,336,104,241) -> Matrix(1,-2,2,-3) Matrix(335,768,188,431) -> Matrix(1,0,0,1) Matrix(95,216,84,191) -> Matrix(1,0,0,1) Matrix(191,432,-340,-769) -> Matrix(1,-2,0,1) Matrix(119,264,32,71) -> Matrix(1,2,0,1) Matrix(23,48,-12,-25) -> Matrix(1,0,0,1) Matrix(311,576,-480,-889) -> Matrix(15,4,-4,-1) Matrix(313,576,144,265) -> Matrix(1,0,-4,1) Matrix(119,216,92,167) -> Matrix(1,0,2,1) Matrix(241,432,188,337) -> Matrix(1,0,-2,1) Matrix(431,768,188,335) -> Matrix(1,0,-2,1) Matrix(433,768,-676,-1199) -> Matrix(11,-8,-4,3) Matrix(95,168,108,191) -> Matrix(1,-2,2,-3) Matrix(97,168,56,97) -> Matrix(1,2,0,1) Matrix(71,120,-100,-169) -> Matrix(1,0,0,1) Matrix(73,120,132,217) -> Matrix(1,0,2,1) Matrix(265,432,192,313) -> Matrix(3,2,4,3) Matrix(119,192,44,71) -> Matrix(3,2,4,3) Matrix(121,192,-196,-311) -> Matrix(7,2,-4,-1) Matrix(47,72,-32,-49) -> Matrix(1,0,8,1) Matrix(599,864,-816,-1177) -> Matrix(1,0,-6,1) Matrix(1201,1728,768,1105) -> Matrix(21,-4,16,-3) Matrix(385,552,-468,-671) -> Matrix(1,0,-6,1) Matrix(169,240,288,409) -> Matrix(1,0,-4,1) Matrix(577,816,408,577) -> Matrix(5,-2,8,-3) Matrix(409,576,120,169) -> Matrix(7,-2,4,-1) Matrix(121,168,-224,-311) -> Matrix(1,0,-4,1) Matrix(313,432,192,265) -> Matrix(7,-2,4,-1) Matrix(193,264,-280,-383) -> Matrix(7,-2,4,-1) Matrix(71,96,88,119) -> Matrix(5,-2,8,-3) Matrix(73,96,92,121) -> Matrix(1,0,0,1) Matrix(167,216,92,119) -> Matrix(5,-4,4,-3) Matrix(337,432,188,241) -> Matrix(1,0,0,1) Matrix(527,672,-716,-913) -> Matrix(1,0,-2,1) Matrix(455,576,-816,-1033) -> Matrix(3,-2,-4,3) Matrix(457,576,96,121) -> Matrix(11,-14,4,-5) Matrix(215,264,136,167) -> Matrix(5,-4,4,-3) Matrix(217,264,60,73) -> Matrix(3,-2,2,-1) Matrix(143,168,40,47) -> Matrix(3,-2,2,-1) Matrix(145,168,208,241) -> Matrix(1,0,2,1) Matrix(191,216,84,95) -> Matrix(1,0,-2,1) Matrix(191,168,108,95) -> Matrix(1,-2,0,1) Matrix(361,312,140,121) -> Matrix(1,-8,2,-15) Matrix(143,120,56,47) -> Matrix(1,2,2,5) Matrix(407,336,-728,-601) -> Matrix(3,2,-2,-1) Matrix(263,216,28,23) -> Matrix(1,0,2,1) Matrix(119,96,88,71) -> Matrix(1,-2,2,-3) Matrix(121,96,92,73) -> Matrix(1,0,2,1) Matrix(311,240,92,71) -> Matrix(3,-2,2,-1) Matrix(95,72,-128,-97) -> Matrix(1,-2,0,1) Matrix(4343,3192,1664,1223) -> Matrix(1,0,2,1) Matrix(265,192,432,313) -> Matrix(1,0,2,1) Matrix(167,120,32,23) -> Matrix(1,4,0,1) Matrix(409,288,240,169) -> Matrix(3,-2,2,-1) Matrix(241,168,208,145) -> Matrix(1,0,0,1) Matrix(1729,1200,1108,769) -> Matrix(7,-6,6,-5) Matrix(71,48,-108,-73) -> Matrix(1,-6,0,1) Matrix(2255,1464,516,335) -> Matrix(5,22,2,9) Matrix(263,168,36,23) -> Matrix(3,8,-2,-5) Matrix(457,288,192,121) -> Matrix(1,2,-6,-11) Matrix(193,120,156,97) -> Matrix(1,2,0,1) Matrix(313,192,432,265) -> Matrix(3,4,8,11) Matrix(119,72,-200,-121) -> Matrix(3,4,-4,-5) Matrix(4391,2592,1340,791) -> Matrix(7,8,6,7) Matrix(1751,1032,772,455) -> Matrix(3,2,-2,-1) Matrix(409,240,288,169) -> Matrix(5,4,6,5) Matrix(289,168,332,193) -> Matrix(3,2,4,3) Matrix(167,96,40,23) -> Matrix(1,2,0,1) Matrix(169,96,44,25) -> Matrix(1,2,0,1) Matrix(1199,672,1968,1103) -> Matrix(1,0,4,1) Matrix(2063,1152,428,239) -> Matrix(19,22,6,7) 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(1,0,2,1) Matrix(311,-168,224,-121) -> Matrix(1,-2,2,-3) Matrix(601,-336,728,-407) -> Matrix(1,-2,2,-3) Matrix(769,-432,340,-191) -> Matrix(1,-2,0,1) Matrix(745,-432,288,-167) -> Matrix(1,-4,2,-7) Matrix(121,-72,200,-119) -> Matrix(1,0,4,1) Matrix(2833,-1728,864,-527) -> Matrix(19,-6,16,-5) Matrix(311,-192,196,-121) -> Matrix(5,-4,4,-3) Matrix(265,-168,112,-71) -> Matrix(1,0,-4,1) Matrix(673,-432,148,-95) -> Matrix(9,2,4,1) Matrix(335,-216,76,-49) -> Matrix(7,-2,4,-1) Matrix(383,-264,280,-193) -> Matrix(5,-2,8,-3) Matrix(311,-216,36,-25) -> Matrix(1,0,-4,1) Matrix(169,-120,100,-71) -> Matrix(7,-2,4,-1) Matrix(263,-192,100,-73) -> Matrix(5,-2,8,-3) Matrix(409,-312,156,-119) -> Matrix(1,0,0,1) Matrix(215,-168,32,-25) -> Matrix(5,-2,-2,1) Matrix(817,-672,524,-431) -> Matrix(7,-6,6,-5) Matrix(697,-576,144,-119) -> Matrix(13,-10,4,-3) Matrix(265,-336,56,-71) -> Matrix(5,-8,2,-3) Matrix(1129,-1440,432,-551) -> Matrix(1,0,2,1) Matrix(841,-1152,192,-263) -> Matrix(5,-4,4,-3) Matrix(49,-72,32,-47) -> Matrix(9,-8,8,-7) Matrix(719,-1128,276,-433) -> Matrix(5,-6,6,-7) Matrix(623,-1104,136,-241) -> Matrix(9,2,4,1) Matrix(25,-48,12,-23) -> Matrix(1,-2,0,1) Matrix(383,-840,88,-193) -> Matrix(7,-2,4,-1) Matrix(25,-72,8,-23) -> Matrix(5,-4,4,-3) Matrix(25,-144,4,-23) -> Matrix(1,-10,0,1) 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: 32 Genus: 17 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -6/1 -5/1 -3/1 -2/1 -9/5 -6/5 -1/1 -2/3 0/1 1/2 2/3 3/4 1/1 6/5 5/4 4/3 3/2 12/7 9/5 2/1 9/4 12/5 5/2 8/3 3/1 4/1 9/2 24/5 5/1 6/1 8/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -7/1 0/1 1/1 1/0 -6/1 1/0 -5/1 -2/1 -1/1 1/0 -14/3 -1/1 1/0 -9/2 -1/1 -4/1 -1/2 1/0 -3/1 0/1 -8/3 1/0 -13/5 -1/1 0/1 1/0 -18/7 1/0 -5/2 -1/2 1/0 -12/5 0/1 -7/3 0/1 1/2 1/1 -16/7 1/2 1/0 -9/4 1/0 -11/5 -1/1 -1/2 0/1 -2/1 0/1 1/0 -13/7 -1/1 -1/2 0/1 -24/13 0/1 -11/6 1/2 1/0 -9/5 0/1 -16/9 1/2 1/0 -23/13 1/1 2/1 1/0 -7/4 1/0 -12/7 0/1 -5/3 -1/1 0/1 1/0 -13/8 1/0 -8/5 -1/2 -3/2 0/1 -4/3 1/2 -9/7 1/1 -14/11 1/2 1/1 -19/15 1/2 2/3 1/1 -24/19 1/1 -5/4 1/0 -11/9 0/1 1/1 1/0 -6/5 1/2 1/0 -7/6 1/2 1/0 -8/7 1/2 1/0 -1/1 0/1 1/1 1/0 -6/7 1/0 -5/6 -3/2 1/0 -9/11 0/1 -4/5 1/0 -3/4 1/0 -8/11 1/0 -5/7 -1/1 0/1 1/0 -12/17 0/1 -7/10 1/2 1/0 -16/23 1/2 1/0 -9/13 1/1 -2/3 1/0 -9/14 -3/1 -16/25 -11/4 -5/2 -7/11 -5/2 -7/3 -2/1 -12/19 -2/1 -5/8 -3/2 -8/13 -3/2 -3/5 -1/1 -4/7 -1/2 1/0 -9/16 1/0 -5/9 -1/1 -1/2 0/1 -6/11 -1/2 1/0 -1/2 -1/2 1/0 0/1 0/1 1/2 1/2 1/0 3/5 0/1 5/8 1/0 7/11 0/1 1/3 1/2 16/25 1/2 1/0 9/14 0/1 2/3 0/1 1/2 9/13 0/1 7/10 1/4 1/2 5/7 0/1 1/3 1/2 8/11 1/2 3/4 1/2 4/5 1/2 5/6 1/2 1/0 6/7 1/2 1/1 0/1 1/2 1/1 7/6 1/2 1/0 6/5 1/2 1/0 5/4 1/2 14/11 1/0 9/7 0/1 13/10 1/4 1/2 4/3 1/2 3/2 1/1 8/5 3/2 13/8 3/2 18/11 3/2 1/0 5/3 1/1 3/2 2/1 17/10 3/2 1/0 12/7 2/1 7/4 1/0 16/9 1/2 1/0 25/14 1/2 1/0 9/5 1/1 11/6 3/2 7/4 2/1 1/0 13/6 -1/2 -1/4 24/11 0/1 11/5 0/1 1/2 1/1 9/4 1/0 16/7 -1/2 1/0 23/10 -1/2 1/0 7/3 -1/1 -1/2 0/1 19/8 -1/4 12/5 0/1 5/2 1/4 1/2 13/5 1/2 2/3 1/1 8/3 1/2 11/4 3/4 3/1 1/1 7/2 3/2 1/0 18/5 3/2 1/0 11/3 1/1 3/2 2/1 15/4 1/0 4/1 3/2 1/0 9/2 2/1 14/3 5/2 19/4 11/4 24/5 3/1 5/1 3/1 4/1 1/0 11/2 11/2 1/0 6/1 1/0 7/1 -3/1 -2/1 1/0 8/1 -1/2 1/0 1/0 1/0 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(7,72,-4,-41) (-7/1,1/0) -> (-23/13,-7/4) Hyperbolic Matrix(7,48,8,55) (-7/1,-6/1) -> (6/7,1/1) Hyperbolic Matrix(31,168,-12,-65) (-6/1,-5/1) -> (-13/5,-18/7) Hyperbolic Matrix(71,336,-56,-265) (-5/1,-14/3) -> (-14/11,-19/15) Hyperbolic Matrix(31,144,48,223) (-14/3,-9/2) -> (9/14,2/3) Hyperbolic Matrix(17,72,4,17) (-9/2,-4/1) -> (4/1,9/2) Hyperbolic Matrix(7,24,-12,-41) (-4/1,-3/1) -> (-3/5,-4/7) Hyperbolic Matrix(17,48,-28,-79) (-3/1,-8/3) -> (-8/13,-3/5) Hyperbolic Matrix(55,144,76,199) (-8/3,-13/5) -> (5/7,8/11) 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(31,72,-28,-65) (-7/3,-16/7) -> (-8/7,-1/1) Hyperbolic Matrix(127,288,56,127) (-16/7,-9/4) -> (9/4,16/7) 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(233,432,48,89) (-13/7,-24/13) -> (24/5,5/1) 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(161,288,-232,-415) (-9/5,-16/9) -> (-16/23,-9/13) Hyperbolic Matrix(271,480,424,751) (-16/9,-23/13) -> (7/11,16/25) 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(103,168,-84,-137) (-5/3,-13/8) -> (-5/4,-11/9) Hyperbolic Matrix(119,192,44,71) (-13/8,-8/5) -> (8/3,11/4) Hyperbolic Matrix(31,48,20,31) (-8/5,-3/2) -> (3/2,8/5) Hyperbolic Matrix(17,24,12,17) (-3/2,-4/3) -> (4/3,3/2) Hyperbolic Matrix(55,72,-68,-89) (-4/3,-9/7) -> (-9/11,-4/5) Hyperbolic Matrix(113,144,164,209) (-9/7,-14/11) -> (2/3,9/13) Hyperbolic Matrix(569,720,260,329) (-19/15,-24/19) -> (24/11,11/5) Hyperbolic Matrix(457,576,96,121) (-24/19,-5/4) -> (19/4,24/5) 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(271,312,152,175) (-7/6,-8/7) -> (16/9,25/14) Hyperbolic Matrix(55,48,8,7) (-1/1,-6/7) -> (6/1,7/1) Hyperbolic Matrix(113,96,20,17) (-6/7,-5/6) -> (11/2,6/1) Hyperbolic Matrix(175,144,96,79) (-5/6,-9/11) -> (9/5,11/6) Hyperbolic Matrix(31,24,40,31) (-4/5,-3/4) -> (3/4,4/5) Hyperbolic Matrix(65,48,88,65) (-3/4,-8/11) -> (8/11,3/4) Hyperbolic Matrix(199,144,76,55) (-8/11,-5/7) -> (13/5,8/3) Hyperbolic Matrix(409,288,240,169) (-12/17,-7/10) -> (17/10,12/7) Hyperbolic Matrix(689,480,300,209) (-7/10,-16/23) -> (16/7,23/10) Hyperbolic Matrix(209,144,164,113) (-9/13,-2/3) -> (14/11,9/7) Hyperbolic Matrix(223,144,48,31) (-2/3,-9/14) -> (9/2,14/3) Hyperbolic Matrix(449,288,700,449) (-9/14,-16/25) -> (16/25,9/14) 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(233,144,144,89) (-5/8,-8/13) -> (8/5,13/8) Hyperbolic Matrix(169,96,44,25) (-4/7,-9/16) -> (15/4,4/1) Hyperbolic Matrix(257,144,116,65) (-9/16,-5/9) -> (11/5,9/4) Hyperbolic Matrix(217,120,132,73) (-5/9,-6/11) -> (18/11,5/3) Hyperbolic Matrix(89,48,76,41) (-6/11,-1/2) -> (7/6,6/5) Hyperbolic Matrix(1,0,4,1) (-1/2,0/1) -> (0/1,1/2) Parabolic Matrix(41,-24,12,-7) (1/2,3/5) -> (3/1,7/2) Hyperbolic Matrix(79,-48,28,-17) (3/5,5/8) -> (11/4,3/1) Hyperbolic Matrix(265,-168,112,-71) (5/8,7/11) -> (7/3,19/8) Hyperbolic Matrix(415,-288,232,-161) (9/13,7/10) -> (25/14,9/5) Hyperbolic Matrix(169,-120,100,-71) (7/10,5/7) -> (5/3,17/10) Hyperbolic Matrix(89,-72,68,-55) (4/5,5/6) -> (13/10,4/3) Hyperbolic Matrix(65,-72,28,-31) (1/1,7/6) -> (23/10,7/3) Hyperbolic Matrix(137,-168,84,-103) (6/5,5/4) -> (13/8,18/11) Hyperbolic Matrix(265,-336,56,-71) (5/4,14/11) -> (14/3,19/4) Hyperbolic Matrix(41,-72,4,-7) (7/4,16/9) -> (8/1,1/0) Hyperbolic Matrix(25,-48,12,-23) (11/6,2/1) -> (2/1,13/6) Parabolic Matrix(65,-168,12,-31) (5/2,13/5) -> (5/1,11/2) Hyperbolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(7,72,-4,-41) -> Matrix(1,1,0,1) Matrix(7,48,8,55) -> Matrix(1,-1,2,-1) Matrix(31,168,-12,-65) -> Matrix(1,1,0,1) Matrix(71,336,-56,-265) -> Matrix(1,0,2,1) Matrix(31,144,48,223) -> Matrix(1,1,2,3) Matrix(17,72,4,17) -> Matrix(3,1,2,1) Matrix(7,24,-12,-41) -> Matrix(1,1,-2,-1) Matrix(17,48,-28,-79) -> Matrix(3,-1,-2,1) Matrix(55,144,76,199) -> Matrix(1,1,2,3) Matrix(47,120,56,143) -> Matrix(1,0,2,1) Matrix(49,120,20,49) -> Matrix(1,0,4,1) Matrix(71,168,-112,-265) -> Matrix(9,-2,-4,1) Matrix(31,72,-28,-65) -> Matrix(1,-1,2,-1) Matrix(127,288,56,127) -> Matrix(1,-1,0,1) Matrix(119,264,32,71) -> Matrix(1,2,0,1) Matrix(23,48,-12,-25) -> Matrix(1,0,0,1) Matrix(233,432,48,89) -> Matrix(7,3,2,1) Matrix(313,576,144,265) -> Matrix(1,0,-4,1) Matrix(119,216,92,167) -> Matrix(1,0,2,1) Matrix(161,288,-232,-415) -> Matrix(1,-1,2,-1) Matrix(271,480,424,751) -> Matrix(1,-1,2,-1) Matrix(97,168,56,97) -> Matrix(1,2,0,1) Matrix(71,120,-100,-169) -> Matrix(1,0,0,1) Matrix(103,168,-84,-137) -> Matrix(1,1,0,1) Matrix(119,192,44,71) -> Matrix(3,2,4,3) Matrix(31,48,20,31) -> Matrix(5,1,4,1) Matrix(17,24,12,17) -> Matrix(3,-1,4,-1) Matrix(55,72,-68,-89) -> Matrix(1,-1,2,-1) Matrix(113,144,164,209) -> Matrix(1,-1,4,-3) Matrix(569,720,260,329) -> Matrix(1,-1,4,-3) Matrix(457,576,96,121) -> Matrix(11,-14,4,-5) Matrix(217,264,60,73) -> Matrix(3,-2,2,-1) Matrix(143,168,40,47) -> Matrix(3,-2,2,-1) Matrix(271,312,152,175) -> Matrix(1,-1,2,-1) Matrix(55,48,8,7) -> Matrix(1,-3,0,1) Matrix(113,96,20,17) -> Matrix(1,7,0,1) Matrix(175,144,96,79) -> Matrix(3,1,2,1) Matrix(31,24,40,31) -> Matrix(1,-1,2,-1) Matrix(65,48,88,65) -> Matrix(1,1,2,3) Matrix(199,144,76,55) -> Matrix(1,-1,2,-1) Matrix(409,288,240,169) -> Matrix(3,-2,2,-1) Matrix(689,480,300,209) -> Matrix(1,-1,0,1) Matrix(209,144,164,113) -> Matrix(1,-1,0,1) Matrix(223,144,48,31) -> Matrix(5,17,2,7) Matrix(449,288,700,449) -> Matrix(1,3,-2,-5) Matrix(263,168,36,23) -> Matrix(3,8,-2,-5) Matrix(457,288,192,121) -> Matrix(1,2,-6,-11) Matrix(233,144,144,89) -> Matrix(1,3,0,1) Matrix(169,96,44,25) -> Matrix(1,2,0,1) Matrix(257,144,116,65) -> Matrix(1,1,0,1) Matrix(217,120,132,73) -> Matrix(1,2,0,1) Matrix(89,48,76,41) -> Matrix(1,1,0,1) Matrix(1,0,4,1) -> Matrix(1,0,2,1) Matrix(41,-24,12,-7) -> Matrix(1,1,0,1) Matrix(79,-48,28,-17) -> Matrix(3,-1,4,-1) Matrix(265,-168,112,-71) -> Matrix(1,0,-4,1) Matrix(415,-288,232,-161) -> Matrix(3,-1,4,-1) Matrix(169,-120,100,-71) -> Matrix(7,-2,4,-1) Matrix(89,-72,68,-55) -> Matrix(1,-1,4,-3) Matrix(65,-72,28,-31) -> Matrix(1,-1,0,1) Matrix(137,-168,84,-103) -> Matrix(1,1,0,1) Matrix(265,-336,56,-71) -> Matrix(5,-8,2,-3) Matrix(41,-72,4,-7) -> Matrix(1,-1,0,1) Matrix(25,-48,12,-23) -> Matrix(1,-2,0,1) Matrix(65,-168,12,-31) -> Matrix(9,-5,2,-1) 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 1/0 1 2 -5/1 0 12 -9/2 -1/1 4 4 -4/1 0 6 -3/1 0/1 2 4 -8/3 1/0 1 6 -5/2 (-1/2,1/0) 0 12 -12/5 0/1 7 2 -7/3 0 12 -9/4 1/0 1 4 -2/1 (0/1,1/0) 0 6 -3/2 0/1 4 4 -4/3 1/2 1 6 -5/4 1/0 1 12 -6/5 (1/2,1/0) 0 2 -1/1 0 12 -4/5 1/0 1 6 -3/4 1/0 1 4 -2/3 1/0 3 6 -7/11 0 12 -12/19 -2/1 7 2 -5/8 -3/2 1 12 -3/5 -1/1 2 4 -4/7 0 6 -5/9 0 12 -1/2 (-1/2,1/0) 0 12 0/1 0/1 1 2 1/2 (1/2,1/0) 0 12 3/5 0/1 2 4 5/8 1/0 1 12 7/11 0 12 9/14 0/1 4 4 2/3 (0/1,1/2) 0 6 3/4 1/2 1 4 4/5 1/2 1 6 5/6 (1/2,1/0) 0 12 6/7 1/2 1 2 1/1 0 12 7/6 (1/2,1/0) 0 12 6/5 (1/2,1/0) 0 2 5/4 1/2 1 12 9/7 0/1 2 4 4/3 1/2 1 6 3/2 1/1 4 4 2/1 1/0 1 6 9/4 1/0 1 4 16/7 0 6 7/3 0 12 19/8 -1/4 1 12 12/5 0/1 7 2 5/2 (1/4,1/2) 0 12 13/5 0 12 8/3 1/2 1 6 11/4 3/4 1 12 3/1 1/1 2 4 7/2 (3/2,1/0) 0 12 18/5 (3/2,1/0) 0 2 11/3 0 12 15/4 1/0 1 4 4/1 0 6 9/2 2/1 4 4 14/3 5/2 3 6 5/1 0 12 11/2 (11/2,1/0) 0 12 6/1 1/0 5 2 1/0 1/0 1 12 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,12,0,-1) (-6/1,1/0) -> (-6/1,1/0) Reflection Matrix(7,36,8,41) (-6/1,-5/1) -> (6/7,1/1) Glide Reflection Matrix(23,108,36,169) (-5/1,-9/2) -> (7/11,9/14) Glide Reflection Matrix(17,72,4,17) (-9/2,-4/1) -> (4/1,9/2) Hyperbolic Matrix(7,24,-12,-41) (-4/1,-3/1) -> (-3/5,-4/7) Hyperbolic Matrix(31,84,24,65) (-3/1,-8/3) -> (9/7,4/3) Glide Reflection Matrix(23,60,28,73) (-8/3,-5/2) -> (4/5,5/6) Glide Reflection 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(89,204,24,55) (-7/3,-9/4) -> (11/3,15/4) Glide Reflection Matrix(17,36,-8,-17) (-9/4,-2/1) -> (-9/4,-2/1) Reflection Matrix(7,12,-4,-7) (-2/1,-3/2) -> (-2/1,-3/2) Reflection Matrix(17,24,12,17) (-3/2,-4/3) -> (4/3,3/2) Hyperbolic Matrix(65,84,24,31) (-4/3,-5/4) -> (8/3,11/4) Glide Reflection Matrix(49,60,-40,-49) (-5/4,-6/5) -> (-5/4,-6/5) Reflection Matrix(73,84,20,23) (-6/5,-1/1) -> (18/5,11/3) Glide Reflection Matrix(73,60,28,23) (-1/1,-4/5) -> (13/5,8/3) Glide Reflection Matrix(31,24,40,31) (-4/5,-3/4) -> (3/4,4/5) Hyperbolic Matrix(17,12,-24,-17) (-3/4,-2/3) -> (-3/4,-2/3) Reflection Matrix(169,108,36,23) (-2/3,-7/11) -> (14/3,5/1) Glide Reflection Matrix(457,288,192,121) (-12/19,-5/8) -> (19/8,12/5) Hyperbolic Matrix(97,60,76,47) (-5/8,-3/5) -> (5/4,9/7) Glide Reflection Matrix(193,108,84,47) (-4/7,-5/9) -> (16/7,7/3) Glide Reflection Matrix(65,36,56,31) (-5/9,-1/2) -> (1/1,7/6) Glide Reflection Matrix(1,0,4,1) (-1/2,0/1) -> (0/1,1/2) Parabolic Matrix(41,-24,12,-7) (1/2,3/5) -> (3/1,7/2) Hyperbolic Matrix(79,-48,28,-17) (3/5,5/8) -> (11/4,3/1) Hyperbolic Matrix(265,-168,112,-71) (5/8,7/11) -> (7/3,19/8) Hyperbolic Matrix(55,-36,84,-55) (9/14,2/3) -> (9/14,2/3) Reflection Matrix(17,-12,24,-17) (2/3,3/4) -> (2/3,3/4) Reflection Matrix(71,-60,84,-71) (5/6,6/7) -> (5/6,6/7) Reflection Matrix(71,-84,60,-71) (7/6,6/5) -> (7/6,6/5) Reflection Matrix(49,-60,40,-49) (6/5,5/4) -> (6/5,5/4) Reflection Matrix(7,-12,4,-7) (3/2,2/1) -> (3/2,2/1) Reflection Matrix(17,-36,8,-17) (2/1,9/4) -> (2/1,9/4) Reflection Matrix(121,-276,32,-73) (9/4,16/7) -> (15/4,4/1) Glide Reflection Matrix(65,-168,12,-31) (5/2,13/5) -> (5/1,11/2) Hyperbolic Matrix(71,-252,20,-71) (7/2,18/5) -> (7/2,18/5) Reflection Matrix(55,-252,12,-55) (9/2,14/3) -> (9/2,14/3) Reflection Matrix(23,-132,4,-23) (11/2,6/1) -> (11/2,6/1) Reflection Matrix(-1,12,0,1) (6/1,1/0) -> (6/1,1/0) Reflection IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,12,0,-1) -> Matrix(1,1,0,-1) (-6/1,1/0) -> (-1/2,1/0) Matrix(7,36,8,41) -> Matrix(1,2,2,3) Matrix(23,108,36,169) -> Matrix(1,1,2,1) Matrix(17,72,4,17) -> Matrix(3,1,2,1) Matrix(7,24,-12,-41) -> Matrix(1,1,-2,-1) (-1/1,0/1).(-1/2,1/0) Matrix(31,84,24,65) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(23,60,28,73) -> Matrix(1,1,2,1) Matrix(49,120,20,49) -> Matrix(1,0,4,1) 0/1 Matrix(71,168,-112,-265) -> Matrix(9,-2,-4,1) Matrix(89,204,24,55) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(17,36,-8,-17) -> Matrix(1,0,0,-1) (-9/4,-2/1) -> (0/1,1/0) Matrix(7,12,-4,-7) -> Matrix(1,0,0,-1) (-2/1,-3/2) -> (0/1,1/0) Matrix(17,24,12,17) -> Matrix(3,-1,4,-1) 1/2 Matrix(65,84,24,31) -> Matrix(3,-2,4,-3) *** -> (1/2,1/1) Matrix(49,60,-40,-49) -> Matrix(-1,1,0,1) (-5/4,-6/5) -> (1/2,1/0) Matrix(73,84,20,23) -> Matrix(3,-1,2,-1) Matrix(73,60,28,23) -> Matrix(1,1,2,1) Matrix(31,24,40,31) -> Matrix(1,-1,2,-1) (0/1,1/1).(1/2,1/0) Matrix(17,12,-24,-17) -> Matrix(1,0,0,-1) (-3/4,-2/3) -> (0/1,1/0) Matrix(169,108,36,23) -> Matrix(5,13,2,5) Matrix(457,288,192,121) -> Matrix(1,2,-6,-11) Matrix(97,60,76,47) -> Matrix(1,1,0,-1) *** -> (-1/2,1/0) Matrix(193,108,84,47) -> Matrix(1,1,0,-1) *** -> (-1/2,1/0) Matrix(65,36,56,31) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(1,0,4,1) -> Matrix(1,0,2,1) 0/1 Matrix(41,-24,12,-7) -> Matrix(1,1,0,1) 1/0 Matrix(79,-48,28,-17) -> Matrix(3,-1,4,-1) 1/2 Matrix(265,-168,112,-71) -> Matrix(1,0,-4,1) 0/1 Matrix(55,-36,84,-55) -> Matrix(1,0,4,-1) (9/14,2/3) -> (0/1,1/2) Matrix(17,-12,24,-17) -> Matrix(1,0,4,-1) (2/3,3/4) -> (0/1,1/2) Matrix(71,-60,84,-71) -> Matrix(-1,1,0,1) (5/6,6/7) -> (1/2,1/0) Matrix(71,-84,60,-71) -> Matrix(-1,1,0,1) (7/6,6/5) -> (1/2,1/0) Matrix(49,-60,40,-49) -> Matrix(-1,1,0,1) (6/5,5/4) -> (1/2,1/0) Matrix(7,-12,4,-7) -> Matrix(-1,2,0,1) (3/2,2/1) -> (1/1,1/0) Matrix(17,-36,8,-17) -> Matrix(1,0,0,-1) (2/1,9/4) -> (0/1,1/0) Matrix(121,-276,32,-73) -> Matrix(-1,1,0,1) *** -> (1/2,1/0) Matrix(65,-168,12,-31) -> Matrix(9,-5,2,-1) Matrix(71,-252,20,-71) -> Matrix(-1,3,0,1) (7/2,18/5) -> (3/2,1/0) Matrix(55,-252,12,-55) -> Matrix(9,-20,4,-9) (9/2,14/3) -> (2/1,5/2) Matrix(23,-132,4,-23) -> Matrix(-1,11,0,1) (11/2,6/1) -> (11/2,1/0) Matrix(-1,12,0,1) -> Matrix(-1,1,0,1) (6/1,1/0) -> (1/2,1/0) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.