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 -11/6 -5/3 -3/2 -4/3 -11/9 -7/6 -1/1 -5/6 -3/4 -7/10 -2/3 -23/36 -5/9 -1/2 -11/24 -4/9 -3/8 -1/3 -11/36 -3/10 -3/11 -1/4 -2/9 -5/24 -1/5 -1/6 -1/7 -1/8 -1/9 0/1 1/8 1/7 1/6 2/11 1/5 2/9 1/4 3/11 2/7 7/24 3/10 1/3 4/11 3/8 2/5 5/12 4/9 1/2 5/9 4/7 7/12 2/3 7/10 3/4 4/5 5/6 1/1 7/6 4/3 3/2 5/3 11/6 2/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -2/1 1/0 -11/6 1/0 -9/5 -3/1 -2/1 1/0 -25/14 -3/2 1/0 -16/9 -1/1 -7/4 -1/1 -19/11 -2/1 -1/1 1/0 -12/7 -1/1 1/0 -17/10 -1/2 1/0 -5/3 -1/1 1/1 -23/14 -1/2 1/0 -41/25 -1/1 0/1 1/0 -18/11 1/0 -13/8 -1/1 -8/5 0/1 1/0 -11/7 -1/1 0/1 1/0 -25/16 0/1 -14/9 0/1 -3/2 -1/2 1/0 -13/9 -1/1 -23/16 0/1 -10/7 1/0 -7/5 -2/1 -1/1 1/0 -18/13 1/0 -11/8 -1/1 -4/3 -1/1 -13/10 -1/2 1/0 -9/7 -1/1 -1/2 0/1 -14/11 -1/2 -5/4 0/1 -11/9 -1/1 -17/14 -1/2 1/0 -23/19 -1/2 -1/3 0/1 -6/5 1/0 -7/6 -1/1 -8/7 -1/1 -1/2 -1/1 -1/1 0/1 1/0 -7/8 0/1 -6/7 -1/2 -5/6 0/1 -9/11 0/1 1/2 1/1 -4/5 0/1 1/0 -11/14 1/2 1/0 -18/23 1/0 -7/9 -1/1 1/1 -10/13 1/0 -3/4 0/1 -11/15 1/1 -19/26 3/2 1/0 -8/11 0/1 1/0 -13/18 1/0 -18/25 1/0 -5/7 -2/1 -1/1 1/0 -17/24 -1/1 -12/17 -1/1 -1/2 -7/10 -1/2 1/0 -2/3 0/1 -9/14 1/2 1/0 -25/39 1/1 -16/25 0/1 1/1 -23/36 1/1 -7/11 0/1 1/1 1/0 -12/19 0/1 1/2 -5/8 1/1 -8/13 2/1 1/0 -11/18 1/0 -3/5 0/1 1/1 1/0 -10/17 1/0 -7/12 1/0 -4/7 -1/1 1/0 -13/23 -1/1 -1/2 0/1 -9/16 0/1 -14/25 1/0 -5/9 -1/1 1/1 -6/11 1/0 -1/2 -1/2 1/0 -6/13 1/0 -11/24 1/0 -5/11 -3/1 -2/1 1/0 -4/9 -1/1 -15/34 -1/2 1/0 -11/25 -1/1 -1/2 0/1 -7/16 0/1 -10/23 1/0 -3/7 -1/1 0/1 1/0 -8/19 0/1 1/0 -5/12 1/0 -2/5 1/0 -7/18 -1/1 -12/31 -1/1 1/0 -5/13 -2/1 -1/1 1/0 -23/60 -1/1 -18/47 1/0 -13/34 -3/2 1/0 -8/21 -1/1 -3/8 -1/1 -4/11 -2/1 1/0 -1/3 -1/1 -4/13 -1/2 0/1 -11/36 0/1 -18/59 1/0 -7/23 -1/1 0/1 1/0 -3/10 -1/2 1/0 -5/17 -1/1 0/1 1/0 -7/24 -1/1 -2/7 -1/2 -5/18 0/1 -3/11 0/1 1/1 1/0 -4/15 -1/1 -1/4 -1/1 -3/13 -1/1 -2/3 -1/2 -11/48 -1/2 -8/35 -1/2 -2/5 -5/22 -1/2 -1/4 -2/9 0/1 -7/32 0/1 -5/23 -1/1 -1/2 0/1 -3/14 -1/2 1/0 -4/19 -1/2 0/1 -5/24 0/1 -6/29 1/2 -1/5 -1/1 0/1 1/0 -2/11 1/0 -1/6 -1/1 -2/13 -1/2 -1/7 -1/1 -1/2 0/1 -1/8 0/1 -1/9 -1/1 0/1 -1/1 0/1 1/8 0/1 1/7 -1/1 0/1 1/0 1/6 -1/1 2/11 -1/2 1/5 -1/1 -1/2 0/1 3/14 -1/2 1/0 5/23 -1/1 0/1 1/0 2/9 0/1 3/13 -2/1 -1/1 1/0 1/4 -1/1 4/15 -1/1 3/11 -1/2 -1/3 0/1 5/18 0/1 2/7 1/0 7/24 -1/1 5/17 -1/1 -1/2 0/1 3/10 -1/2 1/0 1/3 -1/1 5/14 -3/4 -1/2 9/25 -1/1 -3/4 -2/3 13/36 -2/3 4/11 -2/3 -1/2 3/8 -1/1 5/13 -1/1 -2/3 -1/2 7/18 -1/1 2/5 -1/2 5/12 -1/2 3/7 -1/1 -1/2 0/1 10/23 -1/2 7/16 0/1 11/25 -1/1 0/1 1/0 4/9 -1/1 5/11 -2/3 -3/5 -1/2 1/2 -1/2 1/0 7/13 -2/3 -3/5 -1/2 13/24 -1/2 6/11 -1/2 5/9 -1/1 -1/3 14/25 -1/2 9/16 0/1 13/23 -1/1 0/1 1/0 4/7 -1/1 -1/2 7/12 -1/2 3/5 -1/2 -1/3 0/1 11/18 -1/2 8/13 -1/2 -2/5 5/8 -1/3 7/11 -1/2 -1/3 0/1 2/3 0/1 9/13 -1/1 0/1 1/0 25/36 -1/1 16/23 -1/1 0/1 7/10 -1/2 1/0 12/17 -1/1 1/0 17/24 -1/1 5/7 -1/1 -2/3 -1/2 13/18 -1/2 8/11 -1/2 0/1 11/15 -1/3 3/4 0/1 10/13 -1/2 7/9 -1/1 -1/3 18/23 -1/2 11/14 -1/2 -1/4 15/19 -1/3 -1/4 0/1 19/24 0/1 4/5 -1/2 0/1 9/11 -1/3 -1/4 0/1 5/6 0/1 6/7 1/0 7/8 0/1 1/1 -1/1 -1/2 0/1 8/7 -1/1 1/0 7/6 -1/1 6/5 -1/2 17/14 -1/2 1/0 28/23 -1/1 0/1 11/9 -1/1 5/4 0/1 14/11 1/0 23/18 -1/1 9/7 -1/1 0/1 1/0 13/10 -1/2 1/0 4/3 -1/1 19/14 -3/4 -1/2 34/25 -1/2 49/36 -1/1 15/11 -1/1 -2/3 -1/2 11/8 -1/1 18/13 -1/2 7/5 -1/1 -2/3 -1/2 17/12 -1/2 10/7 -1/2 23/16 0/1 36/25 -1/1 0/1 13/9 -1/1 16/11 -2/3 -1/2 3/2 -1/2 1/0 20/13 -2/3 -1/2 37/24 -1/2 17/11 -1/2 -2/5 -1/3 14/9 0/1 39/25 -1/1 0/1 1/0 25/16 0/1 11/7 -1/1 -1/2 0/1 19/12 -1/2 8/5 -1/2 0/1 21/13 -1/1 0/1 1/0 13/8 -1/1 18/11 -1/2 5/3 -1/1 -1/3 22/13 -1/2 61/36 0/1 39/23 -1/1 -1/2 0/1 17/10 -1/2 1/0 12/7 -1/1 -1/2 31/18 -1/1 19/11 -1/1 -2/3 -1/2 7/4 -1/1 16/9 -1/1 41/23 -1/1 -2/3 -1/2 25/14 -3/4 -1/2 34/19 -3/4 43/24 -2/3 9/5 -2/3 -3/5 -1/2 11/6 -1/2 13/7 -1/2 -1/3 0/1 2/1 -1/2 1/0 0/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,4,0,1) (-2/1,1/0) -> (2/1,1/0) Parabolic Matrix(121,224,-168,-311) (-2/1,-11/6) -> (-13/18,-18/25) Hyperbolic Matrix(73,132,120,217) (-11/6,-9/5) -> (3/5,11/18) Hyperbolic Matrix(407,728,-336,-601) (-9/5,-25/14) -> (-17/14,-23/19) Hyperbolic Matrix(191,340,-432,-769) (-25/14,-16/9) -> (-4/9,-15/34) Hyperbolic Matrix(25,44,96,169) (-16/9,-7/4) -> (1/4,4/15) Hyperbolic Matrix(23,40,96,167) (-7/4,-19/11) -> (3/13,1/4) Hyperbolic Matrix(167,288,-432,-745) (-19/11,-12/7) -> (-12/31,-5/13) Hyperbolic Matrix(169,288,240,409) (-12/7,-17/10) -> (7/10,12/17) Hyperbolic Matrix(119,200,-72,-121) (-17/10,-5/3) -> (-5/3,-23/14) Parabolic Matrix(1199,1968,672,1103) (-23/14,-41/25) -> (41/23,25/14) Hyperbolic Matrix(527,864,-1728,-2833) (-41/25,-18/11) -> (-18/59,-7/23) Hyperbolic Matrix(265,432,192,313) (-18/11,-13/8) -> (11/8,18/13) Hyperbolic Matrix(121,196,-192,-311) (-13/8,-8/5) -> (-12/19,-5/8) Hyperbolic Matrix(71,112,-168,-265) (-8/5,-11/7) -> (-3/7,-8/19) Hyperbolic Matrix(23,36,168,263) (-11/7,-25/16) -> (1/8,1/7) Hyperbolic Matrix(95,148,-432,-673) (-25/16,-14/9) -> (-2/9,-7/32) Hyperbolic Matrix(49,76,-216,-335) (-14/9,-3/2) -> (-5/22,-2/9) Hyperbolic Matrix(193,280,-264,-383) (-3/2,-13/9) -> (-11/15,-19/26) Hyperbolic Matrix(25,36,-216,-311) (-13/9,-23/16) -> (-1/8,-1/9) Hyperbolic Matrix(145,208,168,241) (-23/16,-10/7) -> (6/7,7/8) Hyperbolic Matrix(71,100,-120,-169) (-10/7,-7/5) -> (-3/5,-10/17) Hyperbolic Matrix(23,32,120,167) (-7/5,-18/13) -> (2/11,1/5) Hyperbolic Matrix(313,432,192,265) (-18/13,-11/8) -> (13/8,18/11) Hyperbolic Matrix(73,100,-192,-263) (-11/8,-4/3) -> (-8/21,-3/8) Hyperbolic Matrix(119,156,-312,-409) (-4/3,-13/10) -> (-13/34,-8/21) Hyperbolic Matrix(71,92,240,311) (-13/10,-9/7) -> (5/17,3/10) Hyperbolic Matrix(25,32,-168,-215) (-9/7,-14/11) -> (-2/13,-1/7) Hyperbolic Matrix(73,92,96,121) (-14/11,-5/4) -> (3/4,10/13) Hyperbolic Matrix(71,88,96,119) (-5/4,-11/9) -> (11/15,3/4) Hyperbolic Matrix(431,524,-672,-817) (-11/9,-17/14) -> (-9/14,-25/39) Hyperbolic Matrix(119,144,-576,-697) (-23/19,-6/5) -> (-6/29,-1/5) Hyperbolic Matrix(47,56,120,143) (-6/5,-7/6) -> (7/18,2/5) Hyperbolic Matrix(289,332,168,193) (-7/6,-8/7) -> (12/7,31/18) Hyperbolic Matrix(95,108,168,191) (-8/7,-1/1) -> (13/23,4/7) Hyperbolic Matrix(95,84,216,191) (-1/1,-7/8) -> (7/16,11/25) Hyperbolic Matrix(241,208,168,145) (-7/8,-6/7) -> (10/7,23/16) Hyperbolic Matrix(47,40,168,143) (-6/7,-5/6) -> (5/18,2/7) Hyperbolic Matrix(73,60,264,217) (-5/6,-9/11) -> (3/11,5/18) Hyperbolic Matrix(193,156,120,97) (-9/11,-4/5) -> (8/5,21/13) Hyperbolic Matrix(71,56,-336,-265) (-4/5,-11/14) -> (-3/14,-4/19) Hyperbolic Matrix(551,432,-1440,-1129) (-11/14,-18/23) -> (-18/47,-13/34) Hyperbolic Matrix(241,188,432,337) (-18/23,-7/9) -> (5/9,14/25) Hyperbolic Matrix(119,92,216,167) (-7/9,-10/13) -> (6/11,5/9) Hyperbolic Matrix(121,92,96,73) (-10/13,-3/4) -> (5/4,14/11) Hyperbolic Matrix(119,88,96,71) (-3/4,-11/15) -> (11/9,5/4) Hyperbolic Matrix(263,192,-1152,-841) (-19/26,-8/11) -> (-8/35,-5/22) Hyperbolic Matrix(265,192,432,313) (-8/11,-13/18) -> (11/18,8/13) Hyperbolic Matrix(145,104,336,241) (-18/25,-5/7) -> (3/7,10/23) Hyperbolic Matrix(169,120,576,409) (-5/7,-17/24) -> (7/24,5/17) Hyperbolic Matrix(577,408,816,577) (-17/24,-12/17) -> (12/17,17/24) Hyperbolic Matrix(409,288,240,169) (-12/17,-7/10) -> (17/10,12/7) Hyperbolic Matrix(47,32,-72,-49) (-7/10,-2/3) -> (-2/3,-9/14) Parabolic Matrix(1729,1108,1200,769) (-25/39,-16/25) -> (36/25,13/9) Hyperbolic Matrix(1201,768,1728,1105) (-16/25,-23/36) -> (25/36,16/23) Hyperbolic Matrix(433,276,-1128,-719) (-23/36,-7/11) -> (-5/13,-23/60) Hyperbolic Matrix(215,136,264,167) (-7/11,-12/19) -> (4/5,9/11) Hyperbolic Matrix(71,44,192,119) (-5/8,-8/13) -> (4/11,3/8) Hyperbolic Matrix(313,192,432,265) (-8/13,-11/18) -> (13/18,8/11) Hyperbolic Matrix(217,132,120,73) (-11/18,-3/5) -> (9/5,11/6) Hyperbolic Matrix(409,240,288,169) (-10/17,-7/12) -> (17/12,10/7) Hyperbolic Matrix(97,56,168,97) (-7/12,-4/7) -> (4/7,7/12) Hyperbolic Matrix(191,108,168,95) (-4/7,-13/23) -> (1/1,8/7) Hyperbolic Matrix(241,136,-1104,-623) (-13/23,-9/16) -> (-7/32,-5/23) Hyperbolic Matrix(335,188,768,431) (-9/16,-14/25) -> (10/23,7/16) Hyperbolic Matrix(337,188,432,241) (-14/25,-5/9) -> (7/9,18/23) Hyperbolic Matrix(167,92,216,119) (-5/9,-6/11) -> (10/13,7/9) Hyperbolic Matrix(23,12,-48,-25) (-6/11,-1/2) -> (-1/2,-6/13) Parabolic Matrix(313,144,576,265) (-6/13,-11/24) -> (13/24,6/11) Hyperbolic Matrix(193,88,-840,-383) (-11/24,-5/11) -> (-3/13,-11/48) Hyperbolic Matrix(71,32,264,119) (-5/11,-4/9) -> (4/15,3/11) Hyperbolic Matrix(1751,772,1032,455) (-15/34,-11/25) -> (39/23,17/10) Hyperbolic Matrix(191,84,216,95) (-11/25,-7/16) -> (7/8,1/1) Hyperbolic Matrix(431,188,768,335) (-7/16,-10/23) -> (14/25,9/16) Hyperbolic Matrix(313,136,168,73) (-10/23,-3/7) -> (13/7,2/1) Hyperbolic Matrix(457,192,288,121) (-8/19,-5/12) -> (19/12,8/5) Hyperbolic Matrix(49,20,120,49) (-5/12,-2/5) -> (2/5,5/12) Hyperbolic Matrix(143,56,120,47) (-2/5,-7/18) -> (7/6,6/5) Hyperbolic Matrix(361,140,312,121) (-7/18,-12/31) -> (8/7,7/6) Hyperbolic Matrix(4343,1664,3192,1223) (-23/60,-18/47) -> (34/25,49/36) Hyperbolic Matrix(119,44,192,71) (-3/8,-4/11) -> (8/13,5/8) Hyperbolic Matrix(23,8,-72,-25) (-4/11,-1/3) -> (-1/3,-4/13) Parabolic Matrix(313,96,864,265) (-4/13,-11/36) -> (13/36,4/11) Hyperbolic Matrix(4391,1340,2592,791) (-11/36,-18/59) -> (22/13,61/36) Hyperbolic Matrix(119,36,552,167) (-7/23,-3/10) -> (3/14,5/23) Hyperbolic Matrix(311,92,240,71) (-3/10,-5/17) -> (9/7,13/10) Hyperbolic Matrix(409,120,576,169) (-5/17,-7/24) -> (17/24,5/7) Hyperbolic Matrix(97,28,336,97) (-7/24,-2/7) -> (2/7,7/24) Hyperbolic Matrix(143,40,168,47) (-2/7,-5/18) -> (5/6,6/7) Hyperbolic Matrix(217,60,264,73) (-5/18,-3/11) -> (9/11,5/6) Hyperbolic Matrix(119,32,264,71) (-3/11,-4/15) -> (4/9,5/11) Hyperbolic Matrix(169,44,96,25) (-4/15,-1/4) -> (7/4,16/9) Hyperbolic Matrix(167,40,96,23) (-1/4,-3/13) -> (19/11,7/4) Hyperbolic Matrix(2255,516,1464,335) (-11/48,-8/35) -> (20/13,37/24) Hyperbolic Matrix(241,52,672,145) (-5/23,-3/14) -> (5/14,9/25) Hyperbolic Matrix(457,96,576,121) (-4/19,-5/24) -> (19/24,4/5) Hyperbolic Matrix(2063,428,1152,239) (-5/24,-6/29) -> (34/19,43/24) Hyperbolic Matrix(167,32,120,23) (-1/5,-2/11) -> (18/13,7/5) Hyperbolic Matrix(23,4,-144,-25) (-2/11,-1/6) -> (-1/6,-2/13) Parabolic Matrix(263,36,168,23) (-1/7,-1/8) -> (25/16,11/7) Hyperbolic Matrix(263,28,216,23) (-1/9,0/1) -> (28/23,11/9) Hyperbolic Matrix(311,-36,216,-25) (0/1,1/8) -> (23/16,36/25) Hyperbolic Matrix(215,-32,168,-25) (1/7,1/6) -> (23/18,9/7) Hyperbolic Matrix(337,-60,264,-47) (1/6,2/11) -> (14/11,23/18) Hyperbolic Matrix(265,-56,336,-71) (1/5,3/14) -> (11/14,15/19) Hyperbolic Matrix(673,-148,432,-95) (5/23,2/9) -> (14/9,39/25) Hyperbolic Matrix(335,-76,216,-49) (2/9,3/13) -> (17/11,14/9) Hyperbolic Matrix(25,-8,72,-23) (3/10,1/3) -> (1/3,5/14) Parabolic Matrix(2929,-1056,1728,-623) (9/25,13/36) -> (61/36,39/23) Hyperbolic Matrix(263,-100,192,-73) (3/8,5/13) -> (15/11,11/8) Hyperbolic Matrix(745,-288,432,-167) (5/13,7/18) -> (31/18,19/11) Hyperbolic Matrix(265,-112,168,-71) (5/12,3/7) -> (11/7,19/12) Hyperbolic Matrix(769,-340,432,-191) (11/25,4/9) -> (16/9,41/23) Hyperbolic Matrix(25,-12,48,-23) (5/11,1/2) -> (1/2,7/13) Parabolic Matrix(889,-480,576,-311) (7/13,13/24) -> (37/24,17/11) Hyperbolic Matrix(1199,-676,768,-433) (9/16,13/23) -> (39/25,25/16) Hyperbolic Matrix(169,-100,120,-71) (7/12,3/5) -> (7/5,17/12) Hyperbolic Matrix(311,-196,192,-121) (5/8,7/11) -> (21/13,13/8) Hyperbolic Matrix(49,-32,72,-47) (7/11,2/3) -> (2/3,9/13) Parabolic Matrix(1177,-816,864,-599) (9/13,25/36) -> (49/36,15/11) Hyperbolic Matrix(671,-468,552,-385) (16/23,7/10) -> (17/14,28/23) Hyperbolic Matrix(311,-224,168,-121) (5/7,13/18) -> (11/6,13/7) Hyperbolic Matrix(383,-280,264,-193) (8/11,11/15) -> (13/9,16/11) Hyperbolic Matrix(913,-716,672,-527) (18/23,11/14) -> (19/14,34/25) Hyperbolic Matrix(1033,-816,576,-455) (15/19,19/24) -> (43/24,9/5) Hyperbolic Matrix(601,-728,336,-407) (6/5,17/14) -> (25/14,34/19) Hyperbolic Matrix(97,-128,72,-95) (13/10,4/3) -> (4/3,19/14) Parabolic Matrix(73,-108,48,-71) (16/11,3/2) -> (3/2,20/13) Parabolic Matrix(121,-200,72,-119) (18/11,5/3) -> (5/3,22/13) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,4,0,1) -> Matrix(1,0,-2,1) Matrix(121,224,-168,-311) -> Matrix(1,-2,0,1) Matrix(73,132,120,217) -> Matrix(1,2,-2,-3) Matrix(407,728,-336,-601) -> Matrix(1,2,-2,-3) Matrix(191,340,-432,-769) -> Matrix(1,2,-2,-3) Matrix(25,44,96,169) -> Matrix(1,2,-2,-3) Matrix(23,40,96,167) -> Matrix(1,0,0,1) Matrix(167,288,-432,-745) -> Matrix(1,0,0,1) Matrix(169,288,240,409) -> Matrix(1,0,0,1) Matrix(119,200,-72,-121) -> Matrix(1,0,0,1) Matrix(1199,1968,672,1103) -> Matrix(1,2,-2,-3) Matrix(527,864,-1728,-2833) -> Matrix(1,0,0,1) Matrix(265,432,192,313) -> Matrix(1,2,-2,-3) Matrix(121,196,-192,-311) -> Matrix(1,0,2,1) Matrix(71,112,-168,-265) -> Matrix(1,0,0,1) Matrix(23,36,168,263) -> Matrix(1,0,0,1) Matrix(95,148,-432,-673) -> Matrix(1,0,0,1) Matrix(49,76,-216,-335) -> Matrix(1,0,-2,1) Matrix(193,280,-264,-383) -> Matrix(1,2,0,1) Matrix(25,36,-216,-311) -> Matrix(1,0,0,1) Matrix(145,208,168,241) -> Matrix(1,0,0,1) Matrix(71,100,-120,-169) -> Matrix(1,2,0,1) Matrix(23,32,120,167) -> Matrix(1,2,-2,-3) Matrix(313,432,192,265) -> Matrix(1,2,-2,-3) Matrix(73,100,-192,-263) -> Matrix(1,0,0,1) Matrix(119,156,-312,-409) -> Matrix(3,2,-2,-1) Matrix(71,92,240,311) -> Matrix(1,0,0,1) Matrix(25,32,-168,-215) -> Matrix(1,0,0,1) Matrix(73,92,96,121) -> Matrix(1,0,0,1) Matrix(71,88,96,119) -> Matrix(1,0,-2,1) Matrix(431,524,-672,-817) -> Matrix(1,0,2,1) Matrix(119,144,-576,-697) -> Matrix(1,0,2,1) Matrix(47,56,120,143) -> Matrix(1,2,-2,-3) Matrix(289,332,168,193) -> Matrix(1,0,0,1) Matrix(95,108,168,191) -> Matrix(1,0,0,1) Matrix(95,84,216,191) -> Matrix(1,0,0,1) Matrix(241,208,168,145) -> Matrix(1,0,0,1) Matrix(47,40,168,143) -> Matrix(1,0,2,1) Matrix(73,60,264,217) -> Matrix(1,0,-4,1) Matrix(193,156,120,97) -> Matrix(1,0,-2,1) Matrix(71,56,-336,-265) -> Matrix(1,0,-2,1) Matrix(551,432,-1440,-1129) -> Matrix(1,-2,0,1) Matrix(241,188,432,337) -> Matrix(1,0,-2,1) Matrix(119,92,216,167) -> Matrix(1,0,-2,1) Matrix(121,92,96,73) -> Matrix(1,0,0,1) Matrix(119,88,96,71) -> Matrix(1,0,-2,1) Matrix(263,192,-1152,-841) -> Matrix(1,-2,-2,5) Matrix(265,192,432,313) -> Matrix(1,-2,-2,5) Matrix(145,104,336,241) -> Matrix(1,2,-2,-3) Matrix(169,120,576,409) -> Matrix(1,2,-2,-3) Matrix(577,408,816,577) -> Matrix(3,2,-2,-1) Matrix(409,288,240,169) -> Matrix(1,0,0,1) Matrix(47,32,-72,-49) -> Matrix(1,0,2,1) Matrix(1729,1108,1200,769) -> Matrix(1,0,-2,1) Matrix(1201,768,1728,1105) -> Matrix(1,0,-2,1) Matrix(433,276,-1128,-719) -> Matrix(1,-2,0,1) Matrix(215,136,264,167) -> Matrix(1,0,-4,1) Matrix(71,44,192,119) -> Matrix(1,0,-2,1) Matrix(313,192,432,265) -> Matrix(1,-2,-2,5) Matrix(217,132,120,73) -> Matrix(1,2,-2,-3) Matrix(409,240,288,169) -> Matrix(1,-2,-2,5) Matrix(97,56,168,97) -> Matrix(1,2,-2,-3) Matrix(191,108,168,95) -> Matrix(1,0,0,1) Matrix(241,136,-1104,-623) -> Matrix(1,0,0,1) Matrix(335,188,768,431) -> Matrix(1,0,-2,1) Matrix(337,188,432,241) -> Matrix(1,0,-2,1) Matrix(167,92,216,119) -> Matrix(1,0,-2,1) Matrix(23,12,-48,-25) -> Matrix(1,0,0,1) Matrix(313,144,576,265) -> Matrix(1,-2,-2,5) Matrix(193,88,-840,-383) -> Matrix(1,4,-2,-7) Matrix(71,32,264,119) -> Matrix(1,2,-2,-3) Matrix(1751,772,1032,455) -> Matrix(1,0,0,1) Matrix(191,84,216,95) -> Matrix(1,0,0,1) Matrix(431,188,768,335) -> Matrix(1,0,-2,1) Matrix(313,136,168,73) -> Matrix(1,0,-2,1) Matrix(457,192,288,121) -> Matrix(1,0,-2,1) Matrix(49,20,120,49) -> Matrix(1,2,-2,-3) Matrix(143,56,120,47) -> Matrix(1,2,-2,-3) Matrix(361,140,312,121) -> Matrix(1,0,0,1) Matrix(4343,1664,3192,1223) -> Matrix(1,2,-2,-3) Matrix(119,44,192,71) -> Matrix(1,0,-2,1) Matrix(23,8,-72,-25) -> Matrix(1,2,-2,-3) Matrix(313,96,864,265) -> Matrix(5,2,-8,-3) Matrix(4391,1340,2592,791) -> Matrix(1,0,-2,1) Matrix(119,36,552,167) -> Matrix(1,0,0,1) Matrix(311,92,240,71) -> Matrix(1,0,0,1) Matrix(409,120,576,169) -> Matrix(1,2,-2,-3) Matrix(97,28,336,97) -> Matrix(3,2,-2,-1) Matrix(143,40,168,47) -> Matrix(1,0,2,1) Matrix(217,60,264,73) -> Matrix(1,0,-4,1) Matrix(119,32,264,71) -> Matrix(1,2,-2,-3) Matrix(169,44,96,25) -> Matrix(1,2,-2,-3) Matrix(167,40,96,23) -> Matrix(1,0,0,1) Matrix(2255,516,1464,335) -> Matrix(9,4,-16,-7) Matrix(241,52,672,145) -> Matrix(1,2,-2,-3) Matrix(457,96,576,121) -> Matrix(1,0,0,1) Matrix(2063,428,1152,239) -> Matrix(7,-2,-10,3) Matrix(167,32,120,23) -> Matrix(1,2,-2,-3) Matrix(23,4,-144,-25) -> Matrix(1,2,-2,-3) Matrix(263,36,168,23) -> Matrix(1,0,0,1) Matrix(263,28,216,23) -> Matrix(1,0,0,1) Matrix(311,-36,216,-25) -> Matrix(1,0,0,1) Matrix(215,-32,168,-25) -> Matrix(1,0,0,1) Matrix(337,-60,264,-47) -> Matrix(3,2,-2,-1) Matrix(265,-56,336,-71) -> Matrix(1,0,-2,1) Matrix(673,-148,432,-95) -> Matrix(1,0,0,1) Matrix(335,-76,216,-49) -> Matrix(1,0,-2,1) Matrix(25,-8,72,-23) -> Matrix(1,2,-2,-3) Matrix(2929,-1056,1728,-623) -> Matrix(3,2,-2,-1) Matrix(263,-100,192,-73) -> Matrix(1,0,0,1) Matrix(745,-288,432,-167) -> Matrix(1,0,0,1) Matrix(265,-112,168,-71) -> Matrix(1,0,0,1) Matrix(769,-340,432,-191) -> Matrix(1,2,-2,-3) Matrix(25,-12,48,-23) -> Matrix(1,0,0,1) Matrix(889,-480,576,-311) -> Matrix(7,4,-16,-9) Matrix(1199,-676,768,-433) -> Matrix(1,0,0,1) Matrix(169,-100,120,-71) -> Matrix(5,2,-8,-3) Matrix(311,-196,192,-121) -> Matrix(1,0,2,1) Matrix(49,-32,72,-47) -> Matrix(1,0,2,1) Matrix(1177,-816,864,-599) -> Matrix(1,2,-2,-3) Matrix(671,-468,552,-385) -> Matrix(1,0,0,1) Matrix(311,-224,168,-121) -> Matrix(3,2,-8,-5) Matrix(383,-280,264,-193) -> Matrix(5,2,-8,-3) Matrix(913,-716,672,-527) -> Matrix(5,2,-8,-3) Matrix(1033,-816,576,-455) -> Matrix(9,2,-14,-3) Matrix(601,-728,336,-407) -> Matrix(1,2,-2,-3) Matrix(97,-128,72,-95) -> Matrix(1,2,-2,-3) Matrix(73,-108,48,-71) -> Matrix(1,0,0,1) Matrix(121,-200,72,-119) -> 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): 21 Degree of the the map X: 21 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. ----------------------------------------------------------------------- The image of the modular group liftables in PSL(2,Z) equals the image of the pure modular group liftables. ----------------------------------------------------------------------- INFORMATION ON THE IMAGE IN PGL(2,Z) OF THE GROUP OF EXTENDED MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE c d 0/1 (-1/1,0/1) 0 12 1/8 0/1 1 6 1/7 0 12 1/6 -1/1 1 2 2/11 -1/2 1 12 1/5 0 12 3/14 0 6 5/23 0 12 2/9 0/1 1 4 3/13 0 12 1/4 -1/1 1 6 4/15 -1/1 1 4 3/11 0 12 5/18 0/1 3 2 2/7 1/0 1 12 7/24 -1/1 4 2 5/17 0 12 3/10 0 6 1/3 -1/1 1 4 5/14 0 6 9/25 0 12 13/36 -2/3 2 2 4/11 (-2/3,-1/2) 0 12 3/8 -1/1 1 6 5/13 0 12 7/18 -1/1 1 2 2/5 -1/2 1 12 5/12 -1/2 1 2 3/7 0 12 10/23 -1/2 1 12 7/16 0/1 1 6 11/25 0 12 4/9 -1/1 1 4 5/11 0 12 1/2 0 6 7/13 0 12 13/24 -1/2 7 2 6/11 -1/2 1 12 5/9 0 4 14/25 -1/2 1 12 9/16 0/1 1 6 13/23 0 12 4/7 (-1/1,-1/2) 0 12 7/12 -1/2 3 2 3/5 0 12 11/18 -1/2 3 2 8/13 (-1/2,-2/5) 0 12 5/8 -1/3 1 6 7/11 0 12 2/3 0/1 1 4 9/13 0 12 25/36 -1/1 1 2 16/23 (-1/1,0/1) 0 12 7/10 0 6 12/17 (-1/1,1/0) 0 12 17/24 -1/1 4 2 5/7 0 12 13/18 -1/2 3 2 8/11 (-1/2,0/1) 0 12 11/15 -1/3 1 4 3/4 0/1 1 6 10/13 -1/2 1 12 7/9 0 4 18/23 -1/2 1 12 11/14 0 6 15/19 0 12 19/24 0/1 4 2 4/5 (-1/2,0/1) 0 12 9/11 0 12 5/6 0/1 3 2 6/7 1/0 1 12 7/8 0/1 1 6 1/1 0 12 8/7 (-1/1,1/0) 0 12 7/6 -1/1 1 2 6/5 -1/2 1 12 17/14 0 6 28/23 (-1/1,0/1) 0 12 11/9 -1/1 1 4 5/4 0/1 1 6 14/11 1/0 1 12 23/18 -1/1 1 2 9/7 0 12 13/10 0 6 4/3 -1/1 1 4 19/14 0 6 34/25 -1/2 1 12 49/36 -1/1 1 2 15/11 0 12 11/8 -1/1 1 6 18/13 -1/2 1 12 7/5 0 12 17/12 -1/2 3 2 10/7 -1/2 1 12 23/16 0/1 1 6 36/25 (-1/1,0/1) 0 12 13/9 -1/1 1 4 16/11 (-2/3,-1/2) 0 12 3/2 0 6 20/13 (-2/3,-1/2) 0 12 37/24 -1/2 7 2 17/11 0 12 14/9 0/1 1 4 39/25 0 12 25/16 0/1 1 6 11/7 0 12 19/12 -1/2 1 2 8/5 (-1/2,0/1) 0 12 21/13 0 12 13/8 -1/1 1 6 18/11 -1/2 1 12 5/3 0 4 22/13 -1/2 1 12 61/36 0/1 2 2 39/23 0 12 17/10 0 6 12/7 (-1/1,-1/2) 0 12 31/18 -1/1 1 2 19/11 0 12 7/4 -1/1 1 6 16/9 -1/1 1 4 41/23 0 12 25/14 0 6 34/19 -3/4 1 12 43/24 -2/3 4 2 9/5 0 12 11/6 -1/2 3 2 13/7 0 12 2/1 -1/2 1 12 1/0 0/1 1 2 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,0,0,-1) (0/1,1/0) -> (0/1,1/0) Reflection Matrix(311,-36,216,-25) (0/1,1/8) -> (23/16,36/25) Hyperbolic Matrix(263,-36,168,-23) (1/8,1/7) -> (25/16,11/7) Glide Reflection Matrix(215,-32,168,-25) (1/7,1/6) -> (23/18,9/7) Hyperbolic Matrix(337,-60,264,-47) (1/6,2/11) -> (14/11,23/18) Hyperbolic Matrix(167,-32,120,-23) (2/11,1/5) -> (18/13,7/5) Glide Reflection Matrix(265,-56,336,-71) (1/5,3/14) -> (11/14,15/19) Hyperbolic Matrix(241,-52,672,-145) (3/14,5/23) -> (5/14,9/25) Glide Reflection Matrix(673,-148,432,-95) (5/23,2/9) -> (14/9,39/25) Hyperbolic Matrix(335,-76,216,-49) (2/9,3/13) -> (17/11,14/9) Hyperbolic Matrix(167,-40,96,-23) (3/13,1/4) -> (19/11,7/4) Glide Reflection Matrix(169,-44,96,-25) (1/4,4/15) -> (7/4,16/9) Glide Reflection Matrix(119,-32,264,-71) (4/15,3/11) -> (4/9,5/11) Glide Reflection Matrix(217,-60,264,-73) (3/11,5/18) -> (9/11,5/6) Glide Reflection Matrix(143,-40,168,-47) (5/18,2/7) -> (5/6,6/7) Glide Reflection Matrix(97,-28,336,-97) (2/7,7/24) -> (2/7,7/24) Reflection Matrix(409,-120,576,-169) (7/24,5/17) -> (17/24,5/7) Glide Reflection Matrix(311,-92,240,-71) (5/17,3/10) -> (9/7,13/10) Glide Reflection Matrix(25,-8,72,-23) (3/10,1/3) -> (1/3,5/14) Parabolic Matrix(2929,-1056,1728,-623) (9/25,13/36) -> (61/36,39/23) Hyperbolic Matrix(287,-104,792,-287) (13/36,4/11) -> (13/36,4/11) Reflection Matrix(119,-44,192,-71) (4/11,3/8) -> (8/13,5/8) Glide Reflection Matrix(263,-100,192,-73) (3/8,5/13) -> (15/11,11/8) Hyperbolic Matrix(745,-288,432,-167) (5/13,7/18) -> (31/18,19/11) Hyperbolic Matrix(143,-56,120,-47) (7/18,2/5) -> (7/6,6/5) Glide Reflection Matrix(49,-20,120,-49) (2/5,5/12) -> (2/5,5/12) Reflection Matrix(265,-112,168,-71) (5/12,3/7) -> (11/7,19/12) Hyperbolic Matrix(313,-136,168,-73) (3/7,10/23) -> (13/7,2/1) Glide Reflection Matrix(431,-188,768,-335) (10/23,7/16) -> (14/25,9/16) Glide Reflection Matrix(191,-84,216,-95) (7/16,11/25) -> (7/8,1/1) Glide Reflection Matrix(769,-340,432,-191) (11/25,4/9) -> (16/9,41/23) Hyperbolic Matrix(25,-12,48,-23) (5/11,1/2) -> (1/2,7/13) Parabolic Matrix(889,-480,576,-311) (7/13,13/24) -> (37/24,17/11) Hyperbolic Matrix(287,-156,528,-287) (13/24,6/11) -> (13/24,6/11) Reflection Matrix(167,-92,216,-119) (6/11,5/9) -> (10/13,7/9) Glide Reflection Matrix(337,-188,432,-241) (5/9,14/25) -> (7/9,18/23) Glide Reflection Matrix(1199,-676,768,-433) (9/16,13/23) -> (39/25,25/16) Hyperbolic Matrix(191,-108,168,-95) (13/23,4/7) -> (1/1,8/7) Glide Reflection Matrix(97,-56,168,-97) (4/7,7/12) -> (4/7,7/12) Reflection Matrix(169,-100,120,-71) (7/12,3/5) -> (7/5,17/12) Hyperbolic Matrix(217,-132,120,-73) (3/5,11/18) -> (9/5,11/6) Glide Reflection Matrix(313,-192,432,-265) (11/18,8/13) -> (13/18,8/11) Glide Reflection Matrix(311,-196,192,-121) (5/8,7/11) -> (21/13,13/8) Hyperbolic Matrix(49,-32,72,-47) (7/11,2/3) -> (2/3,9/13) Parabolic Matrix(1177,-816,864,-599) (9/13,25/36) -> (49/36,15/11) Hyperbolic Matrix(1151,-800,1656,-1151) (25/36,16/23) -> (25/36,16/23) Reflection Matrix(671,-468,552,-385) (16/23,7/10) -> (17/14,28/23) Hyperbolic Matrix(409,-288,240,-169) (7/10,12/17) -> (17/10,12/7) Glide Reflection Matrix(577,-408,816,-577) (12/17,17/24) -> (12/17,17/24) Reflection Matrix(311,-224,168,-121) (5/7,13/18) -> (11/6,13/7) Hyperbolic Matrix(383,-280,264,-193) (8/11,11/15) -> (13/9,16/11) Hyperbolic Matrix(119,-88,96,-71) (11/15,3/4) -> (11/9,5/4) Glide Reflection Matrix(121,-92,96,-73) (3/4,10/13) -> (5/4,14/11) Glide Reflection Matrix(913,-716,672,-527) (18/23,11/14) -> (19/14,34/25) Hyperbolic Matrix(1033,-816,576,-455) (15/19,19/24) -> (43/24,9/5) Hyperbolic Matrix(191,-152,240,-191) (19/24,4/5) -> (19/24,4/5) Reflection Matrix(193,-156,120,-97) (4/5,9/11) -> (8/5,21/13) Glide Reflection Matrix(241,-208,168,-145) (6/7,7/8) -> (10/7,23/16) Glide Reflection Matrix(289,-332,168,-193) (8/7,7/6) -> (12/7,31/18) Glide Reflection Matrix(601,-728,336,-407) (6/5,17/14) -> (25/14,34/19) Hyperbolic Matrix(623,-760,432,-527) (28/23,11/9) -> (36/25,13/9) Glide Reflection Matrix(97,-128,72,-95) (13/10,4/3) -> (4/3,19/14) Parabolic Matrix(2449,-3332,1800,-2449) (34/25,49/36) -> (34/25,49/36) Reflection Matrix(313,-432,192,-265) (11/8,18/13) -> (13/8,18/11) Glide Reflection Matrix(239,-340,168,-239) (17/12,10/7) -> (17/12,10/7) Reflection Matrix(73,-108,48,-71) (16/11,3/2) -> (3/2,20/13) Parabolic Matrix(961,-1480,624,-961) (20/13,37/24) -> (20/13,37/24) Reflection Matrix(191,-304,120,-191) (19/12,8/5) -> (19/12,8/5) Reflection Matrix(121,-200,72,-119) (18/11,5/3) -> (5/3,22/13) Parabolic Matrix(1585,-2684,936,-1585) (22/13,61/36) -> (22/13,61/36) Reflection Matrix(985,-1672,552,-937) (39/23,17/10) -> (41/23,25/14) Glide Reflection Matrix(1633,-2924,912,-1633) (34/19,43/24) -> (34/19,43/24) Reflection Matrix(-1,4,0,1) (2/1,1/0) -> (2/1,1/0) Reflection IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,0,0,-1) -> Matrix(-1,0,2,1) (0/1,1/0) -> (-1/1,0/1) Matrix(311,-36,216,-25) -> Matrix(1,0,0,1) Matrix(263,-36,168,-23) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(215,-32,168,-25) -> Matrix(1,0,0,1) Matrix(337,-60,264,-47) -> Matrix(3,2,-2,-1) -1/1 Matrix(167,-32,120,-23) -> Matrix(3,2,-4,-3) *** -> (-1/1,-1/2) Matrix(265,-56,336,-71) -> Matrix(1,0,-2,1) 0/1 Matrix(241,-52,672,-145) -> Matrix(3,2,-4,-3) *** -> (-1/1,-1/2) Matrix(673,-148,432,-95) -> Matrix(1,0,0,1) Matrix(335,-76,216,-49) -> Matrix(1,0,-2,1) 0/1 Matrix(167,-40,96,-23) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(169,-44,96,-25) -> Matrix(3,2,-4,-3) *** -> (-1/1,-1/2) Matrix(119,-32,264,-71) -> Matrix(3,2,-4,-3) *** -> (-1/1,-1/2) Matrix(217,-60,264,-73) -> Matrix(-1,0,6,1) *** -> (-1/3,0/1) Matrix(143,-40,168,-47) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(97,-28,336,-97) -> Matrix(1,2,0,-1) (2/7,7/24) -> (-1/1,1/0) Matrix(409,-120,576,-169) -> Matrix(3,2,-4,-3) *** -> (-1/1,-1/2) Matrix(311,-92,240,-71) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(25,-8,72,-23) -> Matrix(1,2,-2,-3) -1/1 Matrix(2929,-1056,1728,-623) -> Matrix(3,2,-2,-1) -1/1 Matrix(287,-104,792,-287) -> Matrix(7,4,-12,-7) (13/36,4/11) -> (-2/3,-1/2) Matrix(119,-44,192,-71) -> Matrix(-1,0,4,1) *** -> (-1/2,0/1) Matrix(263,-100,192,-73) -> Matrix(1,0,0,1) Matrix(745,-288,432,-167) -> Matrix(1,0,0,1) Matrix(143,-56,120,-47) -> Matrix(3,2,-4,-3) *** -> (-1/1,-1/2) Matrix(49,-20,120,-49) -> Matrix(3,2,-4,-3) (2/5,5/12) -> (-1/1,-1/2) Matrix(265,-112,168,-71) -> Matrix(1,0,0,1) Matrix(313,-136,168,-73) -> Matrix(-1,0,4,1) *** -> (-1/2,0/1) Matrix(431,-188,768,-335) -> Matrix(-1,0,4,1) *** -> (-1/2,0/1) Matrix(191,-84,216,-95) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(769,-340,432,-191) -> Matrix(1,2,-2,-3) -1/1 Matrix(25,-12,48,-23) -> Matrix(1,0,0,1) Matrix(889,-480,576,-311) -> Matrix(7,4,-16,-9) -1/2 Matrix(287,-156,528,-287) -> Matrix(5,2,-12,-5) (13/24,6/11) -> (-1/2,-1/3) Matrix(167,-92,216,-119) -> Matrix(-1,0,4,1) *** -> (-1/2,0/1) Matrix(337,-188,432,-241) -> Matrix(-1,0,4,1) *** -> (-1/2,0/1) Matrix(1199,-676,768,-433) -> Matrix(1,0,0,1) Matrix(191,-108,168,-95) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(97,-56,168,-97) -> Matrix(3,2,-4,-3) (4/7,7/12) -> (-1/1,-1/2) Matrix(169,-100,120,-71) -> Matrix(5,2,-8,-3) -1/2 Matrix(217,-132,120,-73) -> Matrix(3,2,-4,-3) *** -> (-1/1,-1/2) Matrix(313,-192,432,-265) -> Matrix(5,2,-12,-5) *** -> (-1/2,-1/3) Matrix(311,-196,192,-121) -> Matrix(1,0,2,1) 0/1 Matrix(49,-32,72,-47) -> Matrix(1,0,2,1) 0/1 Matrix(1177,-816,864,-599) -> Matrix(1,2,-2,-3) -1/1 Matrix(1151,-800,1656,-1151) -> Matrix(-1,0,2,1) (25/36,16/23) -> (-1/1,0/1) Matrix(671,-468,552,-385) -> Matrix(1,0,0,1) Matrix(409,-288,240,-169) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(577,-408,816,-577) -> Matrix(1,2,0,-1) (12/17,17/24) -> (-1/1,1/0) Matrix(311,-224,168,-121) -> Matrix(3,2,-8,-5) -1/2 Matrix(383,-280,264,-193) -> Matrix(5,2,-8,-3) -1/2 Matrix(119,-88,96,-71) -> Matrix(-1,0,4,1) *** -> (-1/2,0/1) Matrix(121,-92,96,-73) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(913,-716,672,-527) -> Matrix(5,2,-8,-3) -1/2 Matrix(1033,-816,576,-455) -> Matrix(9,2,-14,-3) Matrix(191,-152,240,-191) -> Matrix(-1,0,4,1) (19/24,4/5) -> (-1/2,0/1) Matrix(193,-156,120,-97) -> Matrix(-1,0,4,1) *** -> (-1/2,0/1) Matrix(241,-208,168,-145) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(289,-332,168,-193) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(601,-728,336,-407) -> Matrix(1,2,-2,-3) -1/1 Matrix(623,-760,432,-527) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(97,-128,72,-95) -> Matrix(1,2,-2,-3) -1/1 Matrix(2449,-3332,1800,-2449) -> Matrix(3,2,-4,-3) (34/25,49/36) -> (-1/1,-1/2) Matrix(313,-432,192,-265) -> Matrix(3,2,-4,-3) *** -> (-1/1,-1/2) Matrix(239,-340,168,-239) -> Matrix(-1,0,4,1) (17/12,10/7) -> (-1/2,0/1) Matrix(73,-108,48,-71) -> Matrix(1,0,0,1) Matrix(961,-1480,624,-961) -> Matrix(7,4,-12,-7) (20/13,37/24) -> (-2/3,-1/2) Matrix(191,-304,120,-191) -> Matrix(-1,0,4,1) (19/12,8/5) -> (-1/2,0/1) Matrix(121,-200,72,-119) -> Matrix(1,0,0,1) Matrix(1585,-2684,936,-1585) -> Matrix(-1,0,4,1) (22/13,61/36) -> (-1/2,0/1) Matrix(985,-1672,552,-937) -> Matrix(3,2,-4,-3) *** -> (-1/1,-1/2) Matrix(1633,-2924,912,-1633) -> Matrix(17,12,-24,-17) (34/19,43/24) -> (-3/4,-2/3) Matrix(-1,4,0,1) -> Matrix(-1,0,4,1) (2/1,1/0) -> (-1/2,0/1) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.