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): 1008 Minimal number of generators: 169 Number of equivalence classes of cusps: 60 Genus: 55 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -10/13 -8/13 -1/2 -6/13 -5/12 -79/208 -14/39 -4/13 -1/4 -4/19 -4/23 -9/52 -1/6 -2/13 -2/15 -1/8 -2/17 -3/26 -1/10 -1/11 0/1 1/10 1/9 1/8 1/7 2/13 1/6 2/11 4/21 5/26 1/5 2/9 3/13 1/4 7/26 2/7 4/13 1/3 14/39 5/13 2/5 5/12 11/26 6/13 1/2 7/13 14/25 15/26 8/13 25/39 17/26 2/3 9/13 19/26 10/13 21/26 11/13 23/26 1/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 0/1 1/1 -6/7 2/1 1/0 -11/13 1/0 -16/19 -2/1 1/0 -5/6 0/1 -14/17 0/1 1/2 -9/11 2/3 1/1 -13/16 2/3 -17/21 8/9 1/1 -21/26 1/1 -4/5 1/1 3/2 -7/9 3/1 4/1 -10/13 1/0 -13/17 -3/1 -2/1 -16/21 -2/1 1/0 -19/25 -6/5 -1/1 -3/4 0/1 -11/15 2/3 1/1 -19/26 1/1 -8/11 1/1 3/2 -5/7 1/1 2/1 -17/24 4/1 -29/41 0/1 1/1 -12/17 2/1 1/0 -19/27 3/1 4/1 -26/37 2/1 5/2 -33/47 14/5 3/1 -7/10 4/1 -16/23 8/1 1/0 -9/13 1/0 -2/3 0/1 1/0 -13/20 0/1 -24/37 2/1 1/0 -11/17 0/1 1/1 -9/14 0/1 -34/53 0/1 1/2 -25/39 1/2 -16/25 1/2 1/1 -7/11 0/1 1/1 -19/30 2/1 -31/49 1/1 4/3 -12/19 2/1 1/0 -29/46 0/1 -17/27 1/1 4/3 -22/35 3/2 2/1 -5/8 2/1 -8/13 1/0 -11/18 -6/1 -14/23 -4/1 -7/2 -31/51 -28/9 -3/1 -17/28 -8/3 -3/5 -2/1 -1/1 -16/27 -3/2 -1/1 -29/49 -1/1 -4/5 -13/22 -2/3 -10/17 -1/2 0/1 -7/12 0/1 -25/43 -1/1 0/1 -18/31 -1/2 0/1 -29/50 -2/7 -11/19 -1/5 0/1 -15/26 0/1 -4/7 0/1 1/2 -5/9 1/1 4/3 -6/11 3/1 1/0 -7/13 1/0 -8/15 -4/1 1/0 -9/17 -3/1 -2/1 -1/2 0/1 -6/13 1/0 -11/24 -6/1 -5/11 -3/1 -2/1 -14/31 -2/1 -3/2 -23/51 -1/1 -2/3 -9/20 -2/1 -4/9 -3/2 -1/1 -11/25 -1/1 -2/3 -7/16 -2/3 -10/23 -1/2 -2/5 -3/7 -1/3 0/1 -11/26 0/1 -8/19 0/1 1/8 -5/12 0/1 -12/29 0/1 1/0 -7/17 1/3 2/5 -2/5 1/1 1/0 -5/13 1/0 -8/21 -4/1 1/0 -19/50 -10/3 -49/129 -46/15 -3/1 -79/208 -3/1 -30/79 -3/1 -23/8 -11/29 -3/1 -2/1 -14/37 -5/2 -2/1 -3/8 -2/1 -10/27 -1/1 1/0 -27/73 -1/1 0/1 -44/119 -4/5 -3/4 -17/46 -2/3 -7/19 -1/1 0/1 -4/11 -1/1 -1/2 -9/25 -1/1 0/1 -14/39 -1/2 -19/53 -2/5 -1/3 -5/14 0/1 -6/17 -1/2 0/1 -7/20 0/1 -1/3 0/1 1/1 -4/13 1/0 -7/23 -4/1 -3/1 -10/33 -5/2 -2/1 -13/43 -3/1 -2/1 -3/10 -2/1 -11/37 -2/1 -1/1 -8/27 -3/2 -1/1 -13/44 -4/3 -5/17 -1/1 -4/5 -2/7 0/1 1/0 -7/25 -2/1 -1/1 -12/43 -7/6 -1/1 -29/104 -1/1 -17/61 -1/1 -10/11 -5/18 -2/3 -8/29 -1/4 0/1 -11/40 0/1 -14/51 -1/2 0/1 -3/11 -1/3 0/1 -7/26 0/1 -4/15 0/1 1/4 -5/19 0/1 1/1 -6/23 1/2 2/3 -7/27 1/1 6/5 -1/4 0/1 -4/17 2/1 1/0 -3/13 1/0 -2/9 -1/1 1/0 -7/32 0/1 -12/55 -1/2 0/1 -17/78 0/1 -5/23 -1/1 0/1 -8/37 0/1 1/0 -11/51 -1/1 -2/3 -3/14 0/1 -4/19 0/1 1/4 -9/43 0/1 1/3 -5/24 2/3 -1/5 -1/1 0/1 -5/26 0/1 -4/21 0/1 1/4 -7/37 0/1 1/1 -3/16 0/1 -5/27 0/1 1/1 -2/11 1/1 1/0 -3/17 -1/1 -2/3 -4/23 -1/4 0/1 -9/52 0/1 -5/29 0/1 1/5 -1/6 0/1 -2/13 1/0 -3/20 -2/1 -1/7 -1/1 0/1 -2/15 0/1 1/2 -1/8 0/1 -2/17 -1/2 0/1 -3/26 0/1 -1/9 0/1 1/1 -1/10 0/1 -1/11 -1/1 0/1 0/1 0/1 1/0 1/10 0/1 1/9 -1/1 0/1 1/8 0/1 1/7 0/1 1/1 2/13 1/0 3/19 -2/1 -1/1 1/6 0/1 2/11 -1/1 1/0 3/16 0/1 4/21 -1/4 0/1 5/26 0/1 1/5 0/1 1/1 3/14 0/1 8/37 0/1 1/0 5/23 0/1 1/1 2/9 1/1 1/0 3/13 1/0 4/17 -2/1 1/0 1/4 0/1 5/19 -1/1 0/1 9/34 0/1 4/15 -1/4 0/1 7/26 0/1 3/11 0/1 1/3 8/29 0/1 1/4 5/18 2/3 2/7 0/1 1/0 3/10 2/1 4/13 1/0 5/16 -2/1 11/35 -2/1 -1/1 6/19 -2/1 -3/2 1/3 -1/1 0/1 5/14 0/1 14/39 1/2 23/64 2/3 9/25 0/1 1/1 4/11 1/2 1/1 3/8 2/1 14/37 2/1 5/2 11/29 2/1 3/1 30/79 23/8 3/1 19/50 10/3 8/21 4/1 1/0 5/13 1/0 2/5 -1/1 1/0 5/12 0/1 13/31 -1/3 0/1 21/50 -2/11 29/69 -1/7 0/1 8/19 -1/8 0/1 11/26 0/1 3/7 0/1 1/3 13/30 0/1 23/53 6/19 1/3 10/23 2/5 1/2 7/16 2/3 18/41 3/4 1/1 11/25 2/3 1/1 4/9 1/1 3/2 13/29 1/1 2/1 9/20 2/1 14/31 3/2 2/1 19/42 2/1 5/11 2/1 3/1 6/13 1/0 7/15 -4/1 -3/1 1/2 0/1 9/17 2/1 3/1 8/15 4/1 1/0 7/13 1/0 6/11 -3/1 1/0 11/20 -2/1 5/9 -4/3 -1/1 14/25 -1/1 -3/4 9/16 -2/3 4/7 -1/2 0/1 15/26 0/1 11/19 0/1 1/5 18/31 0/1 1/2 7/12 0/1 17/29 -1/1 0/1 10/17 0/1 1/2 13/22 2/3 16/27 1/1 3/2 3/5 1/1 2/1 8/13 1/0 13/21 -7/1 -6/1 31/50 -16/3 80/129 -71/14 -5/1 129/208 -5/1 49/79 -5/1 -44/9 18/29 -9/2 -4/1 5/8 -2/1 17/27 -4/3 -1/1 46/73 -1/2 0/1 29/46 0/1 12/19 -2/1 1/0 7/11 -1/1 0/1 16/25 -1/1 -1/2 25/39 -1/2 34/53 -1/2 0/1 9/14 0/1 20/31 0/1 1/0 11/17 -1/1 0/1 24/37 -2/1 1/0 13/20 0/1 15/23 -1/1 0/1 17/26 0/1 2/3 0/1 1/0 9/13 1/0 16/23 -8/1 1/0 7/10 -4/1 26/37 -5/2 -2/1 45/64 -2/1 19/27 -4/1 -3/1 31/44 -2/1 43/61 -7/3 -2/1 55/78 -2/1 12/17 -2/1 1/0 17/24 -4/1 22/31 -5/2 -2/1 5/7 -2/1 -1/1 23/32 -4/3 41/57 -2/1 -1/1 18/25 -1/1 1/0 31/43 -8/7 -1/1 13/18 0/1 8/11 -3/2 -1/1 19/26 -1/1 11/15 -1/1 -2/3 14/19 -1/2 0/1 17/23 -2/1 -1/1 20/27 -1/1 -5/6 3/4 0/1 10/13 1/0 17/22 -6/1 41/53 -5/1 -24/5 24/31 -4/1 1/0 7/9 -4/1 -3/1 25/32 -2/1 18/23 -2/1 -3/2 29/37 -2/1 -1/1 69/88 -2/1 40/51 -2/1 1/0 11/14 -2/1 4/5 -3/2 -1/1 21/26 -1/1 17/21 -1/1 -8/9 47/58 -6/7 30/37 -5/6 -4/5 13/16 -2/3 22/27 -1/1 -3/4 9/11 -1/1 -2/3 23/28 -2/5 14/17 -1/2 0/1 19/23 -1/5 0/1 43/52 0/1 24/29 0/1 1/4 5/6 0/1 16/19 2/1 1/0 11/13 1/0 6/7 -2/1 1/0 7/8 -4/3 15/17 -12/11 -1/1 23/26 -1/1 8/9 -1/1 -5/6 1/1 -1/1 0/1 1/0 0/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,2,0,1) (-1/1,1/0) -> (1/1,1/0) Parabolic Matrix(51,44,-182,-157) (-1/1,-6/7) -> (-2/7,-7/25) Hyperbolic Matrix(155,132,182,155) (-6/7,-11/13) -> (11/13,6/7) Hyperbolic Matrix(417,352,494,417) (-11/13,-16/19) -> (16/19,11/13) Hyperbolic Matrix(623,524,988,831) (-16/19,-5/6) -> (29/46,12/19) Hyperbolic Matrix(155,128,-442,-365) (-5/6,-14/17) -> (-6/17,-7/20) Hyperbolic Matrix(625,514,-884,-727) (-14/17,-9/11) -> (-29/41,-12/17) Hyperbolic Matrix(209,170,-702,-571) (-9/11,-13/16) -> (-3/10,-11/37) Hyperbolic Matrix(675,548,-962,-781) (-13/16,-17/21) -> (-33/47,-7/10) Hyperbolic Matrix(883,714,1092,883) (-17/21,-21/26) -> (21/26,17/21) Hyperbolic Matrix(209,168,260,209) (-21/26,-4/5) -> (4/5,21/26) Hyperbolic Matrix(53,42,-130,-103) (-4/5,-7/9) -> (-7/17,-2/5) Hyperbolic Matrix(259,200,-338,-261) (-7/9,-10/13) -> (-10/13,-13/17) Parabolic Matrix(571,436,884,675) (-13/17,-16/21) -> (20/31,11/17) Hyperbolic Matrix(1507,1146,2392,1819) (-16/21,-19/25) -> (17/27,46/73) Hyperbolic Matrix(417,316,962,729) (-19/25,-3/4) -> (13/30,23/53) Hyperbolic Matrix(313,230,-494,-363) (-3/4,-11/15) -> (-7/11,-19/30) Hyperbolic Matrix(571,418,780,571) (-11/15,-19/26) -> (19/26,11/15) Hyperbolic Matrix(417,304,572,417) (-19/26,-8/11) -> (8/11,19/26) Hyperbolic Matrix(105,76,-286,-207) (-8/11,-5/7) -> (-7/19,-4/11) Hyperbolic Matrix(467,332,-806,-573) (-5/7,-17/24) -> (-29/50,-11/19) Hyperbolic Matrix(209,148,442,313) (-17/24,-29/41) -> (7/15,1/2) Hyperbolic Matrix(883,622,-1404,-989) (-12/17,-19/27) -> (-17/27,-22/35) Hyperbolic Matrix(623,438,-2886,-2029) (-19/27,-26/37) -> (-8/37,-11/51) Hyperbolic Matrix(3067,2154,-8294,-5825) (-26/37,-33/47) -> (-27/73,-44/119) Hyperbolic Matrix(261,182,598,417) (-7/10,-16/23) -> (10/23,7/16) Hyperbolic Matrix(415,288,598,415) (-16/23,-9/13) -> (9/13,16/23) Hyperbolic Matrix(53,36,78,53) (-9/13,-2/3) -> (2/3,9/13) Hyperbolic Matrix(261,170,-1196,-779) (-2/3,-13/20) -> (-7/32,-12/55) Hyperbolic Matrix(1509,980,-4082,-2651) (-13/20,-24/37) -> (-44/119,-17/46) Hyperbolic Matrix(469,304,884,573) (-24/37,-11/17) -> (9/17,8/15) Hyperbolic Matrix(469,302,-806,-519) (-11/17,-9/14) -> (-7/12,-25/43) Hyperbolic Matrix(1143,734,1456,935) (-9/14,-34/53) -> (40/51,11/14) Hyperbolic Matrix(2651,1700,4134,2651) (-34/53,-25/39) -> (25/39,34/53) Hyperbolic Matrix(1249,800,1950,1249) (-25/39,-16/25) -> (16/25,25/39) Hyperbolic Matrix(363,232,-1222,-781) (-16/25,-7/11) -> (-11/37,-8/27) Hyperbolic Matrix(1507,954,-2548,-1613) (-19/30,-31/49) -> (-29/49,-13/22) Hyperbolic Matrix(313,198,988,625) (-31/49,-12/19) -> (6/19,1/3) Hyperbolic Matrix(831,524,988,623) (-12/19,-29/46) -> (5/6,16/19) Hyperbolic Matrix(1301,820,-2886,-1819) (-29/46,-17/27) -> (-23/51,-9/20) Hyperbolic Matrix(51,32,-416,-261) (-22/35,-5/8) -> (-1/8,-2/17) Hyperbolic Matrix(207,128,-338,-209) (-5/8,-8/13) -> (-8/13,-11/18) Parabolic Matrix(259,158,936,571) (-11/18,-14/23) -> (8/29,5/18) Hyperbolic Matrix(1039,632,2392,1455) (-14/23,-31/51) -> (23/53,10/23) Hyperbolic Matrix(2341,1422,-6162,-3743) (-31/51,-17/28) -> (-19/50,-49/129) Hyperbolic Matrix(469,284,1118,677) (-17/28,-3/5) -> (13/31,21/50) Hyperbolic Matrix(779,462,-2106,-1249) (-3/5,-16/27) -> (-10/27,-27/73) Hyperbolic Matrix(1767,1046,4654,2755) (-16/27,-29/49) -> (11/29,30/79) Hyperbolic Matrix(105,62,442,261) (-13/22,-10/17) -> (4/17,1/4) Hyperbolic Matrix(157,92,-442,-259) (-10/17,-7/12) -> (-5/14,-6/17) Hyperbolic Matrix(1249,726,1612,937) (-25/43,-18/31) -> (24/31,7/9) Hyperbolic Matrix(989,574,2600,1509) (-18/31,-29/50) -> (19/50,8/21) Hyperbolic Matrix(571,330,988,571) (-11/19,-15/26) -> (15/26,11/19) Hyperbolic Matrix(209,120,364,209) (-15/26,-4/7) -> (4/7,15/26) Hyperbolic Matrix(53,30,-182,-103) (-4/7,-5/9) -> (-5/17,-2/7) Hyperbolic Matrix(51,28,-286,-157) (-5/9,-6/11) -> (-2/11,-3/17) Hyperbolic Matrix(155,84,286,155) (-6/11,-7/13) -> (7/13,6/11) Hyperbolic Matrix(209,112,390,209) (-7/13,-8/15) -> (8/15,7/13) Hyperbolic Matrix(573,304,884,469) (-8/15,-9/17) -> (11/17,24/37) Hyperbolic Matrix(415,218,988,519) (-9/17,-1/2) -> (21/50,29/69) Hyperbolic Matrix(155,72,-338,-157) (-1/2,-6/13) -> (-6/13,-11/24) Parabolic Matrix(469,214,572,261) (-11/24,-5/11) -> (9/11,23/28) Hyperbolic Matrix(261,118,-1378,-623) (-5/11,-14/31) -> (-4/21,-7/37) Hyperbolic Matrix(2495,1126,3224,1455) (-14/31,-23/51) -> (41/53,24/31) Hyperbolic Matrix(103,46,-468,-209) (-9/20,-4/9) -> (-2/9,-7/32) Hyperbolic Matrix(363,160,-1300,-573) (-4/9,-11/25) -> (-7/25,-12/43) Hyperbolic Matrix(155,68,-832,-365) (-11/25,-7/16) -> (-3/16,-5/27) Hyperbolic Matrix(417,182,598,261) (-7/16,-10/23) -> (16/23,7/10) Hyperbolic Matrix(157,68,-598,-259) (-10/23,-3/7) -> (-5/19,-6/23) Hyperbolic Matrix(155,66,364,155) (-3/7,-11/26) -> (11/26,3/7) Hyperbolic Matrix(417,176,988,417) (-11/26,-8/19) -> (8/19,11/26) Hyperbolic Matrix(105,44,-494,-207) (-8/19,-5/12) -> (-3/14,-4/19) Hyperbolic Matrix(415,172,-1508,-625) (-5/12,-12/29) -> (-8/29,-11/40) Hyperbolic Matrix(155,64,-884,-365) (-12/29,-7/17) -> (-3/17,-4/23) Hyperbolic Matrix(51,20,130,51) (-2/5,-5/13) -> (5/13,2/5) Hyperbolic Matrix(209,80,546,209) (-5/13,-8/21) -> (8/21,5/13) Hyperbolic Matrix(1457,554,2054,781) (-8/21,-19/50) -> (17/24,22/31) Hyperbolic Matrix(26833,10192,43264,16433) (-49/129,-79/208) -> (129/208,49/79) Hyperbolic Matrix(26831,10190,43264,16431) (-79/208,-30/79) -> (80/129,129/208) Hyperbolic Matrix(1923,730,2600,987) (-30/79,-11/29) -> (17/23,20/27) Hyperbolic Matrix(417,158,1924,729) (-11/29,-14/37) -> (8/37,5/23) Hyperbolic Matrix(365,138,1378,521) (-14/37,-3/8) -> (9/34,4/15) Hyperbolic Matrix(415,154,-1404,-521) (-3/8,-10/27) -> (-8/27,-13/44) Hyperbolic Matrix(157,58,988,365) (-17/46,-7/19) -> (3/19,1/6) Hyperbolic Matrix(105,38,-572,-207) (-4/11,-9/25) -> (-5/27,-2/11) Hyperbolic Matrix(1091,392,-3042,-1093) (-9/25,-14/39) -> (-14/39,-19/53) Parabolic Matrix(2651,950,3770,1351) (-19/53,-5/14) -> (45/64,19/27) Hyperbolic Matrix(103,36,-598,-209) (-7/20,-1/3) -> (-5/29,-1/6) Hyperbolic Matrix(103,32,-338,-105) (-1/3,-4/13) -> (-4/13,-7/23) Parabolic Matrix(883,268,1196,363) (-7/23,-10/33) -> (14/19,17/23) Hyperbolic Matrix(1301,394,3094,937) (-10/33,-13/43) -> (29/69,8/19) Hyperbolic Matrix(53,16,520,157) (-13/43,-3/10) -> (1/10,1/9) Hyperbolic Matrix(833,246,-2990,-883) (-13/44,-5/17) -> (-17/61,-5/18) Hyperbolic Matrix(1821,508,2054,573) (-12/43,-29/104) -> (23/26,8/9) Hyperbolic Matrix(2963,826,3354,935) (-29/104,-17/61) -> (15/17,23/26) Hyperbolic Matrix(469,130,754,209) (-5/18,-8/29) -> (18/29,5/8) Hyperbolic Matrix(1819,500,2834,779) (-11/40,-14/51) -> (34/53,9/14) Hyperbolic Matrix(51,14,-572,-157) (-14/51,-3/11) -> (-1/11,0/1) Hyperbolic Matrix(155,42,572,155) (-3/11,-7/26) -> (7/26,3/11) Hyperbolic Matrix(209,56,780,209) (-7/26,-4/15) -> (4/15,7/26) Hyperbolic Matrix(53,14,-390,-103) (-4/15,-5/19) -> (-1/7,-2/15) Hyperbolic Matrix(1613,420,2600,677) (-6/23,-7/27) -> (49/79,18/29) Hyperbolic Matrix(623,160,806,207) (-7/27,-1/4) -> (17/22,41/53) Hyperbolic Matrix(261,62,442,105) (-1/4,-4/17) -> (10/17,13/22) Hyperbolic Matrix(103,24,442,103) (-4/17,-3/13) -> (3/13,4/17) Hyperbolic Matrix(53,12,234,53) (-3/13,-2/9) -> (2/9,3/13) Hyperbolic Matrix(1091,238,1664,363) (-12/55,-17/78) -> (17/26,2/3) Hyperbolic Matrix(1561,340,2392,521) (-17/78,-5/23) -> (15/23,17/26) Hyperbolic Matrix(729,158,1924,417) (-5/23,-8/37) -> (14/37,11/29) Hyperbolic Matrix(1299,280,3614,779) (-11/51,-3/14) -> (23/64,9/25) Hyperbolic Matrix(467,98,1482,311) (-4/19,-9/43) -> (11/35,6/19) Hyperbolic Matrix(259,54,494,103) (-9/43,-5/24) -> (1/2,9/17) Hyperbolic Matrix(467,96,754,155) (-5/24,-1/5) -> (13/21,31/50) Hyperbolic Matrix(51,10,260,51) (-1/5,-5/26) -> (5/26,1/5) Hyperbolic Matrix(209,40,1092,209) (-5/26,-4/21) -> (4/21,5/26) Hyperbolic Matrix(53,10,-546,-103) (-7/37,-3/16) -> (-1/10,-1/11) Hyperbolic Matrix(2237,388,2704,469) (-4/23,-9/52) -> (43/52,24/29) Hyperbolic Matrix(2235,386,2704,467) (-9/52,-5/29) -> (19/23,43/52) Hyperbolic Matrix(51,8,-338,-53) (-1/6,-2/13) -> (-2/13,-3/20) Parabolic Matrix(261,38,364,53) (-3/20,-1/7) -> (5/7,23/32) Hyperbolic Matrix(157,20,416,53) (-2/15,-1/8) -> (3/8,14/37) Hyperbolic Matrix(1247,146,1768,207) (-2/17,-3/26) -> (55/78,12/17) Hyperbolic Matrix(1613,184,2288,261) (-3/26,-1/9) -> (43/61,55/78) Hyperbolic Matrix(155,16,494,51) (-1/9,-1/10) -> (5/16,11/35) Hyperbolic Matrix(469,-40,598,-51) (0/1,1/10) -> (69/88,40/51) Hyperbolic Matrix(623,-74,884,-105) (1/9,1/8) -> (31/44,43/61) Hyperbolic Matrix(103,-14,390,-53) (1/8,1/7) -> (5/19,9/34) Hyperbolic Matrix(53,-8,338,-51) (1/7,2/13) -> (2/13,3/19) Parabolic Matrix(157,-28,286,-51) (1/6,2/11) -> (6/11,11/20) Hyperbolic Matrix(365,-68,832,-155) (2/11,3/16) -> (7/16,18/41) Hyperbolic Matrix(623,-118,1378,-261) (3/16,4/21) -> (14/31,19/42) Hyperbolic Matrix(207,-44,494,-105) (1/5,3/14) -> (5/12,13/31) Hyperbolic Matrix(2029,-438,2886,-623) (3/14,8/37) -> (26/37,45/64) Hyperbolic Matrix(209,-46,468,-103) (5/23,2/9) -> (4/9,13/29) Hyperbolic Matrix(259,-68,598,-157) (1/4,5/19) -> (3/7,13/30) Hyperbolic Matrix(1039,-286,1326,-365) (3/11,8/29) -> (18/23,29/37) Hyperbolic Matrix(157,-44,182,-51) (5/18,2/7) -> (6/7,7/8) Hyperbolic Matrix(103,-30,182,-53) (2/7,3/10) -> (9/16,4/7) Hyperbolic Matrix(105,-32,338,-103) (3/10,4/13) -> (4/13,5/16) Parabolic Matrix(259,-92,442,-157) (1/3,5/14) -> (7/12,17/29) Hyperbolic Matrix(1093,-392,3042,-1091) (5/14,14/39) -> (14/39,23/64) Parabolic Matrix(571,-206,1300,-469) (9/25,4/11) -> (18/41,11/25) Hyperbolic Matrix(207,-76,286,-105) (4/11,3/8) -> (13/18,8/11) Hyperbolic Matrix(6449,-2450,10400,-3951) (30/79,19/50) -> (31/50,80/129) Hyperbolic Matrix(103,-42,130,-53) (2/5,5/12) -> (11/14,4/5) Hyperbolic Matrix(209,-92,234,-103) (11/25,4/9) -> (8/9,1/1) Hyperbolic Matrix(677,-304,1040,-467) (13/29,9/20) -> (13/20,15/23) Hyperbolic Matrix(1819,-820,2886,-1301) (9/20,14/31) -> (46/73,29/46) Hyperbolic Matrix(1977,-896,2522,-1143) (19/42,5/11) -> (29/37,69/88) Hyperbolic Matrix(157,-72,338,-155) (5/11,6/13) -> (6/13,7/15) Parabolic Matrix(365,-202,468,-259) (11/20,5/9) -> (7/9,25/32) Hyperbolic Matrix(937,-524,1300,-727) (5/9,14/25) -> (18/25,31/43) Hyperbolic Matrix(677,-380,832,-467) (14/25,9/16) -> (13/16,22/27) Hyperbolic Matrix(573,-332,806,-467) (11/19,18/31) -> (22/31,5/7) Hyperbolic Matrix(519,-302,806,-469) (18/31,7/12) -> (9/14,20/31) Hyperbolic Matrix(729,-428,884,-519) (17/29,10/17) -> (14/17,19/23) Hyperbolic Matrix(521,-308,702,-415) (13/22,16/27) -> (20/27,3/4) Hyperbolic Matrix(1197,-710,1664,-987) (16/27,3/5) -> (41/57,18/25) Hyperbolic Matrix(209,-128,338,-207) (3/5,8/13) -> (8/13,13/21) Parabolic Matrix(989,-622,1404,-883) (5/8,17/27) -> (19/27,31/44) Hyperbolic Matrix(363,-230,494,-313) (12/19,7/11) -> (11/15,14/19) Hyperbolic Matrix(467,-298,572,-365) (7/11,16/25) -> (22/27,9/11) Hyperbolic Matrix(2339,-1518,2886,-1873) (24/37,13/20) -> (47/58,30/37) Hyperbolic Matrix(781,-548,962,-675) (7/10,26/37) -> (30/37,13/16) Hyperbolic Matrix(727,-514,884,-625) (12/17,17/24) -> (23/28,14/17) Hyperbolic Matrix(3223,-2318,3978,-2861) (23/32,41/57) -> (17/21,47/58) Hyperbolic Matrix(571,-412,650,-469) (31/43,13/18) -> (7/8,15/17) Hyperbolic Matrix(261,-200,338,-259) (3/4,10/13) -> (10/13,17/22) Parabolic Matrix(883,-690,1066,-833) (25/32,18/23) -> (24/29,5/6) Hyperbolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,0,1) -> Matrix(1,0,-2,1) Matrix(51,44,-182,-157) -> Matrix(1,-2,0,1) Matrix(155,132,182,155) -> Matrix(1,-4,0,1) Matrix(417,352,494,417) -> Matrix(1,4,0,1) Matrix(623,524,988,831) -> Matrix(1,0,0,1) Matrix(155,128,-442,-365) -> Matrix(1,0,-4,1) Matrix(625,514,-884,-727) -> Matrix(3,-2,2,-1) Matrix(209,170,-702,-571) -> Matrix(1,0,-2,1) Matrix(675,548,-962,-781) -> Matrix(13,-10,4,-3) Matrix(883,714,1092,883) -> Matrix(17,-16,-18,17) Matrix(209,168,260,209) -> Matrix(5,-6,-4,5) Matrix(53,42,-130,-103) -> Matrix(1,-2,2,-3) Matrix(259,200,-338,-261) -> Matrix(1,-6,0,1) Matrix(571,436,884,675) -> Matrix(1,2,0,1) Matrix(1507,1146,2392,1819) -> Matrix(1,2,-2,-3) Matrix(417,316,962,729) -> Matrix(1,0,4,1) Matrix(313,230,-494,-363) -> Matrix(3,-2,2,-1) Matrix(571,418,780,571) -> Matrix(5,-4,-6,5) Matrix(417,304,572,417) -> Matrix(5,-6,-4,5) Matrix(105,76,-286,-207) -> Matrix(1,-2,0,1) Matrix(467,332,-806,-573) -> Matrix(1,-2,-4,9) Matrix(209,148,442,313) -> Matrix(1,-4,0,1) Matrix(883,622,-1404,-989) -> Matrix(3,-8,2,-5) Matrix(623,438,-2886,-2029) -> Matrix(1,-2,-2,5) Matrix(3067,2154,-8294,-5825) -> Matrix(5,-14,-6,17) Matrix(261,182,598,417) -> Matrix(1,-6,2,-11) Matrix(415,288,598,415) -> Matrix(1,-16,0,1) Matrix(53,36,78,53) -> Matrix(1,0,0,1) Matrix(261,170,-1196,-779) -> Matrix(1,0,-2,1) Matrix(1509,980,-4082,-2651) -> Matrix(3,-2,-4,3) Matrix(469,304,884,573) -> Matrix(1,2,0,1) Matrix(469,302,-806,-519) -> Matrix(1,0,-2,1) Matrix(1143,734,1456,935) -> Matrix(5,-2,-2,1) Matrix(2651,1700,4134,2651) -> Matrix(1,0,-4,1) Matrix(1249,800,1950,1249) -> Matrix(3,-2,-4,3) Matrix(363,232,-1222,-781) -> Matrix(1,-2,0,1) Matrix(1507,954,-2548,-1613) -> Matrix(1,0,-2,1) Matrix(313,198,988,625) -> Matrix(3,-4,-2,3) Matrix(831,524,988,623) -> Matrix(1,0,0,1) Matrix(1301,820,-2886,-1819) -> Matrix(1,-2,0,1) Matrix(51,32,-416,-261) -> Matrix(1,-2,0,1) Matrix(207,128,-338,-209) -> Matrix(1,-8,0,1) Matrix(259,158,936,571) -> Matrix(1,4,2,9) Matrix(1039,632,2392,1455) -> Matrix(3,10,8,27) Matrix(2341,1422,-6162,-3743) -> Matrix(19,54,-6,-17) Matrix(469,284,1118,677) -> Matrix(1,2,-4,-7) Matrix(779,462,-2106,-1249) -> Matrix(1,2,-2,-3) Matrix(1767,1046,4654,2755) -> Matrix(17,14,6,5) Matrix(105,62,442,261) -> Matrix(3,2,-2,-1) Matrix(157,92,-442,-259) -> Matrix(1,0,0,1) Matrix(1249,726,1612,937) -> Matrix(7,4,-2,-1) Matrix(989,574,2600,1509) -> Matrix(9,4,2,1) Matrix(571,330,988,571) -> Matrix(1,0,10,1) Matrix(209,120,364,209) -> Matrix(1,0,-4,1) Matrix(53,30,-182,-103) -> Matrix(1,0,-2,1) Matrix(51,28,-286,-157) -> Matrix(1,-2,0,1) Matrix(155,84,286,155) -> Matrix(1,-6,0,1) Matrix(209,112,390,209) -> Matrix(1,8,0,1) Matrix(573,304,884,469) -> Matrix(1,2,0,1) Matrix(415,218,988,519) -> Matrix(1,2,-6,-11) Matrix(155,72,-338,-157) -> Matrix(1,-6,0,1) Matrix(469,214,572,261) -> Matrix(1,4,-2,-7) Matrix(261,118,-1378,-623) -> Matrix(1,2,2,5) Matrix(2495,1126,3224,1455) -> Matrix(9,14,-2,-3) Matrix(103,46,-468,-209) -> Matrix(1,2,-2,-3) Matrix(363,160,-1300,-573) -> Matrix(5,4,-4,-3) Matrix(155,68,-832,-365) -> Matrix(3,2,4,3) Matrix(417,182,598,261) -> Matrix(11,6,-2,-1) Matrix(157,68,-598,-259) -> Matrix(1,0,4,1) Matrix(155,66,364,155) -> Matrix(1,0,6,1) Matrix(417,176,988,417) -> Matrix(1,0,-16,1) Matrix(105,44,-494,-207) -> Matrix(1,0,-4,1) Matrix(415,172,-1508,-625) -> Matrix(1,0,-4,1) Matrix(155,64,-884,-365) -> Matrix(1,0,-4,1) Matrix(51,20,130,51) -> Matrix(1,-2,0,1) Matrix(209,80,546,209) -> Matrix(1,8,0,1) Matrix(1457,554,2054,781) -> Matrix(5,18,-2,-7) Matrix(26833,10192,43264,16433) -> Matrix(119,362,-24,-73) Matrix(26831,10190,43264,16431) -> Matrix(111,328,-22,-65) Matrix(1923,730,2600,987) -> Matrix(3,8,-2,-5) Matrix(417,158,1924,729) -> Matrix(1,2,2,5) Matrix(365,138,1378,521) -> Matrix(1,2,-2,-3) Matrix(415,154,-1404,-521) -> Matrix(3,2,-2,-1) Matrix(157,58,988,365) -> Matrix(3,2,-2,-1) Matrix(105,38,-572,-207) -> Matrix(1,0,2,1) Matrix(1091,392,-3042,-1093) -> Matrix(3,2,-8,-5) Matrix(2651,950,3770,1351) -> Matrix(3,2,-2,-1) Matrix(103,36,-598,-209) -> Matrix(1,0,4,1) Matrix(103,32,-338,-105) -> Matrix(1,-4,0,1) Matrix(883,268,1196,363) -> Matrix(1,2,0,1) Matrix(1301,394,3094,937) -> Matrix(1,2,-6,-11) Matrix(53,16,520,157) -> Matrix(1,2,0,1) Matrix(833,246,-2990,-883) -> Matrix(5,6,-6,-7) Matrix(1821,508,2054,573) -> Matrix(11,12,-12,-13) Matrix(2963,826,3354,935) -> Matrix(23,22,-22,-21) Matrix(469,130,754,209) -> Matrix(7,4,-2,-1) Matrix(1819,500,2834,779) -> Matrix(1,0,0,1) Matrix(51,14,-572,-157) -> Matrix(1,0,2,1) Matrix(155,42,572,155) -> Matrix(1,0,6,1) Matrix(209,56,780,209) -> Matrix(1,0,-8,1) Matrix(53,14,-390,-103) -> Matrix(1,0,-2,1) Matrix(1613,420,2600,677) -> Matrix(19,-14,-4,3) Matrix(623,160,806,207) -> Matrix(1,-6,0,1) Matrix(261,62,442,105) -> Matrix(1,-2,2,-3) Matrix(103,24,442,103) -> Matrix(1,-4,0,1) Matrix(53,12,234,53) -> Matrix(1,2,0,1) Matrix(1091,238,1664,363) -> Matrix(1,0,2,1) Matrix(1561,340,2392,521) -> Matrix(1,0,0,1) Matrix(729,158,1924,417) -> Matrix(5,2,2,1) Matrix(1299,280,3614,779) -> Matrix(3,2,4,3) Matrix(467,98,1482,311) -> Matrix(5,-2,-2,1) Matrix(259,54,494,103) -> Matrix(3,-2,2,-1) Matrix(467,96,754,155) -> Matrix(1,-6,0,1) Matrix(51,10,260,51) -> Matrix(1,0,2,1) Matrix(209,40,1092,209) -> Matrix(1,0,-8,1) Matrix(53,10,-546,-103) -> Matrix(1,0,-2,1) Matrix(2237,388,2704,469) -> Matrix(1,0,8,1) Matrix(2235,386,2704,467) -> Matrix(1,0,-10,1) Matrix(51,8,-338,-53) -> Matrix(1,-2,0,1) Matrix(261,38,364,53) -> Matrix(3,2,-2,-1) Matrix(157,20,416,53) -> Matrix(1,2,0,1) Matrix(1247,146,1768,207) -> Matrix(3,2,-2,-1) Matrix(1613,184,2288,261) -> Matrix(9,-2,-4,1) Matrix(155,16,494,51) -> Matrix(1,-2,0,1) Matrix(469,-40,598,-51) -> Matrix(1,-2,0,1) Matrix(623,-74,884,-105) -> Matrix(5,-2,-2,1) Matrix(103,-14,390,-53) -> Matrix(1,0,-2,1) Matrix(53,-8,338,-51) -> Matrix(1,-2,0,1) Matrix(157,-28,286,-51) -> Matrix(1,-2,0,1) Matrix(365,-68,832,-155) -> Matrix(3,2,4,3) Matrix(623,-118,1378,-261) -> Matrix(5,2,2,1) Matrix(207,-44,494,-105) -> Matrix(1,0,-4,1) Matrix(2029,-438,2886,-623) -> Matrix(5,-2,-2,1) Matrix(209,-46,468,-103) -> Matrix(3,-2,2,-1) Matrix(259,-68,598,-157) -> Matrix(1,0,4,1) Matrix(1039,-286,1326,-365) -> Matrix(5,-2,-2,1) Matrix(157,-44,182,-51) -> Matrix(1,-2,0,1) Matrix(103,-30,182,-53) -> Matrix(1,0,-2,1) Matrix(105,-32,338,-103) -> Matrix(1,-4,0,1) Matrix(259,-92,442,-157) -> Matrix(1,0,0,1) Matrix(1093,-392,3042,-1091) -> Matrix(5,-2,8,-3) Matrix(571,-206,1300,-469) -> Matrix(1,-2,2,-3) Matrix(207,-76,286,-105) -> Matrix(1,-2,0,1) Matrix(6449,-2450,10400,-3951) -> Matrix(31,-98,-6,19) Matrix(103,-42,130,-53) -> Matrix(3,2,-2,-1) Matrix(209,-92,234,-103) -> Matrix(3,-2,-4,3) Matrix(677,-304,1040,-467) -> Matrix(1,-2,0,1) Matrix(1819,-820,2886,-1301) -> Matrix(1,-2,0,1) Matrix(1977,-896,2522,-1143) -> Matrix(1,-4,0,1) Matrix(157,-72,338,-155) -> Matrix(1,-6,0,1) Matrix(365,-202,468,-259) -> Matrix(5,8,-2,-3) Matrix(937,-524,1300,-727) -> Matrix(5,4,-4,-3) Matrix(677,-380,832,-467) -> Matrix(1,0,0,1) Matrix(573,-332,806,-467) -> Matrix(9,-2,-4,1) Matrix(519,-302,806,-469) -> Matrix(1,0,-2,1) Matrix(729,-428,884,-519) -> Matrix(1,0,-4,1) Matrix(521,-308,702,-415) -> Matrix(3,-2,-4,3) Matrix(1197,-710,1664,-987) -> Matrix(3,-4,-2,3) Matrix(209,-128,338,-207) -> Matrix(1,-8,0,1) Matrix(989,-622,1404,-883) -> Matrix(5,8,-2,-3) Matrix(363,-230,494,-313) -> Matrix(1,2,-2,-3) Matrix(467,-298,572,-365) -> Matrix(1,2,-2,-3) Matrix(2339,-1518,2886,-1873) -> Matrix(5,6,-6,-7) Matrix(781,-548,962,-675) -> Matrix(3,10,-4,-13) Matrix(727,-514,884,-625) -> Matrix(1,2,-2,-3) Matrix(3223,-2318,3978,-2861) -> Matrix(9,10,-10,-11) Matrix(571,-412,650,-469) -> Matrix(5,4,-4,-3) Matrix(261,-200,338,-259) -> Matrix(1,-6,0,1) Matrix(883,-690,1066,-833) -> Matrix(1,2,2,5) 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): 56 Degree of the the map X: 56 Degree of the the map Y: 168 ----------------------------------------------------------------------- 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 (0/1,1/0) 0 26 1/10 0/1 1 13 1/9 (-1/1,0/1) 0 26 1/8 0/1 1 13 1/7 (0/1,1/1) 0 26 2/13 1/0 2 2 3/19 (-2/1,-1/1) 0 26 1/6 0/1 1 13 2/11 (-1/1,1/0) 0 26 3/16 0/1 1 13 4/21 (-1/4,0/1) 0 26 5/26 0/1 5 1 1/5 (0/1,1/1) 0 26 3/14 0/1 1 13 8/37 (0/1,1/0) 0 26 5/23 (0/1,1/1) 0 26 2/9 (1/1,1/0) 0 26 3/13 1/0 3 2 4/17 (-2/1,1/0) 0 26 1/4 0/1 1 13 5/19 (-1/1,0/1) 0 26 9/34 0/1 1 13 4/15 (-1/4,0/1) 0 26 7/26 0/1 7 1 3/11 (0/1,1/3) 0 26 8/29 (0/1,1/4) 0 26 5/18 2/3 1 13 2/7 (0/1,1/0) 0 26 3/10 2/1 1 13 4/13 1/0 4 2 5/16 -2/1 1 13 11/35 (-2/1,-1/1) 0 26 6/19 (-2/1,-3/2) 0 26 1/3 (-1/1,0/1) 0 26 5/14 0/1 1 13 14/39 1/2 2 2 23/64 2/3 1 13 9/25 (0/1,1/1) 0 26 4/11 (1/2,1/1) 0 26 3/8 2/1 1 13 14/37 (2/1,5/2) 0 26 11/29 (2/1,3/1) 0 26 30/79 (23/8,3/1) 0 26 19/50 10/3 1 13 8/21 (4/1,1/0) 0 26 5/13 1/0 5 2 2/5 (-1/1,1/0) 0 26 5/12 0/1 1 13 13/31 (-1/3,0/1) 0 26 21/50 -2/11 1 13 29/69 (-1/7,0/1) 0 26 8/19 (-1/8,0/1) 0 26 11/26 0/1 11 1 3/7 (0/1,1/3) 0 26 13/30 0/1 1 13 23/53 (6/19,1/3) 0 26 10/23 (2/5,1/2) 0 26 7/16 2/3 1 13 18/41 (3/4,1/1) 0 26 11/25 (2/3,1/1) 0 26 4/9 (1/1,3/2) 0 26 13/29 (1/1,2/1) 0 26 9/20 2/1 1 13 14/31 (3/2,2/1) 0 26 19/42 2/1 1 13 5/11 (2/1,3/1) 0 26 6/13 1/0 6 2 7/15 (-4/1,-3/1) 0 26 1/2 0/1 1 13 9/17 (2/1,3/1) 0 26 8/15 (4/1,1/0) 0 26 7/13 1/0 7 2 6/11 (-3/1,1/0) 0 26 11/20 -2/1 1 13 5/9 (-4/3,-1/1) 0 26 14/25 (-1/1,-3/4) 0 26 9/16 -2/3 1 13 4/7 (-1/2,0/1) 0 26 15/26 0/1 7 1 11/19 (0/1,1/5) 0 26 18/31 (0/1,1/2) 0 26 7/12 0/1 1 13 17/29 (-1/1,0/1) 0 26 10/17 (0/1,1/2) 0 26 13/22 2/3 1 13 16/27 (1/1,3/2) 0 26 3/5 (1/1,2/1) 0 26 8/13 1/0 8 2 13/21 (-7/1,-6/1) 0 26 31/50 -16/3 1 13 80/129 (-71/14,-5/1) 0 26 129/208 -5/1 23 1 49/79 (-5/1,-44/9) 0 26 18/29 (-9/2,-4/1) 0 26 5/8 -2/1 1 13 17/27 (-4/3,-1/1) 0 26 46/73 (-1/2,0/1) 0 26 29/46 0/1 1 13 12/19 (-2/1,1/0) 0 26 7/11 (-1/1,0/1) 0 26 16/25 (-1/1,-1/2) 0 26 25/39 -1/2 1 2 34/53 (-1/2,0/1) 0 26 9/14 0/1 1 13 20/31 (0/1,1/0) 0 26 11/17 (-1/1,0/1) 0 26 24/37 (-2/1,1/0) 0 26 13/20 0/1 1 13 15/23 (-1/1,0/1) 0 26 17/26 0/1 1 1 2/3 (0/1,1/0) 0 26 9/13 1/0 8 2 16/23 (-8/1,1/0) 0 26 7/10 -4/1 1 13 26/37 (-5/2,-2/1) 0 26 45/64 -2/1 1 13 19/27 (-4/1,-3/1) 0 26 31/44 -2/1 1 13 43/61 (-7/3,-2/1) 0 26 55/78 -2/1 3 1 12/17 (-2/1,1/0) 0 26 17/24 -4/1 1 13 22/31 (-5/2,-2/1) 0 26 5/7 (-2/1,-1/1) 0 26 23/32 -4/3 1 13 41/57 (-2/1,-1/1) 0 26 18/25 (-1/1,1/0) 0 26 31/43 (-8/7,-1/1) 0 26 13/18 0/1 1 13 8/11 (-3/2,-1/1) 0 26 19/26 -1/1 5 1 11/15 (-1/1,-2/3) 0 26 14/19 (-1/2,0/1) 0 26 17/23 (-2/1,-1/1) 0 26 20/27 (-1/1,-5/6) 0 26 3/4 0/1 1 13 10/13 1/0 6 2 17/22 -6/1 1 13 41/53 (-5/1,-24/5) 0 26 24/31 (-4/1,1/0) 0 26 7/9 (-4/1,-3/1) 0 26 25/32 -2/1 1 13 18/23 (-2/1,-3/2) 0 26 29/37 (-2/1,-1/1) 0 26 69/88 -2/1 1 13 40/51 (-2/1,1/0) 0 26 11/14 -2/1 1 13 4/5 (-3/2,-1/1) 0 26 21/26 -1/1 11 1 17/21 (-1/1,-8/9) 0 26 47/58 -6/7 1 13 30/37 (-5/6,-4/5) 0 26 13/16 -2/3 1 13 22/27 (-1/1,-3/4) 0 26 9/11 (-1/1,-2/3) 0 26 23/28 -2/5 1 13 14/17 (-1/2,0/1) 0 26 19/23 (-1/5,0/1) 0 26 43/52 0/1 9 1 24/29 (0/1,1/4) 0 26 5/6 0/1 1 13 16/19 (2/1,1/0) 0 26 11/13 1/0 4 2 6/7 (-2/1,1/0) 0 26 7/8 -4/3 1 13 15/17 (-12/11,-1/1) 0 26 23/26 -1/1 17 1 8/9 (-1/1,-5/6) 0 26 1/1 (-1/1,0/1) 0 26 1/0 0/1 1 1 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(469,-40,598,-51) (0/1,1/10) -> (69/88,40/51) Hyperbolic Matrix(155,-16,494,-51) (1/10,1/9) -> (5/16,11/35) Glide Reflection Matrix(623,-74,884,-105) (1/9,1/8) -> (31/44,43/61) Hyperbolic Matrix(103,-14,390,-53) (1/8,1/7) -> (5/19,9/34) Hyperbolic Matrix(53,-8,338,-51) (1/7,2/13) -> (2/13,3/19) Parabolic Matrix(467,-74,650,-103) (3/19,1/6) -> (5/7,23/32) Glide Reflection Matrix(157,-28,286,-51) (1/6,2/11) -> (6/11,11/20) Hyperbolic Matrix(365,-68,832,-155) (2/11,3/16) -> (7/16,18/41) Hyperbolic Matrix(623,-118,1378,-261) (3/16,4/21) -> (14/31,19/42) Hyperbolic Matrix(209,-40,1092,-209) (4/21,5/26) -> (4/21,5/26) Reflection Matrix(51,-10,260,-51) (5/26,1/5) -> (5/26,1/5) Reflection Matrix(207,-44,494,-105) (1/5,3/14) -> (5/12,13/31) Hyperbolic Matrix(2029,-438,2886,-623) (3/14,8/37) -> (26/37,45/64) Hyperbolic Matrix(729,-158,1924,-417) (8/37,5/23) -> (14/37,11/29) Glide Reflection Matrix(209,-46,468,-103) (5/23,2/9) -> (4/9,13/29) Hyperbolic Matrix(53,-12,234,-53) (2/9,3/13) -> (2/9,3/13) Reflection Matrix(103,-24,442,-103) (3/13,4/17) -> (3/13,4/17) Reflection Matrix(261,-62,442,-105) (4/17,1/4) -> (10/17,13/22) Glide Reflection Matrix(259,-68,598,-157) (1/4,5/19) -> (3/7,13/30) Hyperbolic Matrix(521,-138,1378,-365) (9/34,4/15) -> (3/8,14/37) Glide Reflection Matrix(209,-56,780,-209) (4/15,7/26) -> (4/15,7/26) Reflection Matrix(155,-42,572,-155) (7/26,3/11) -> (7/26,3/11) Reflection Matrix(1039,-286,1326,-365) (3/11,8/29) -> (18/23,29/37) Hyperbolic Matrix(469,-130,754,-209) (8/29,5/18) -> (18/29,5/8) Glide Reflection Matrix(157,-44,182,-51) (5/18,2/7) -> (6/7,7/8) Hyperbolic Matrix(103,-30,182,-53) (2/7,3/10) -> (9/16,4/7) Hyperbolic Matrix(105,-32,338,-103) (3/10,4/13) -> (4/13,5/16) Parabolic Matrix(831,-262,1976,-623) (11/35,6/19) -> (29/69,8/19) Glide Reflection Matrix(365,-116,494,-157) (6/19,1/3) -> (14/19,17/23) Glide Reflection Matrix(259,-92,442,-157) (1/3,5/14) -> (7/12,17/29) Hyperbolic Matrix(1093,-392,3042,-1091) (5/14,14/39) -> (14/39,23/64) Parabolic Matrix(2341,-842,3328,-1197) (23/64,9/25) -> (45/64,19/27) Glide Reflection Matrix(571,-206,1300,-469) (9/25,4/11) -> (18/41,11/25) Hyperbolic Matrix(207,-76,286,-105) (4/11,3/8) -> (13/18,8/11) Hyperbolic Matrix(1923,-730,2600,-987) (11/29,30/79) -> (17/23,20/27) Glide Reflection Matrix(6449,-2450,10400,-3951) (30/79,19/50) -> (31/50,80/129) Hyperbolic Matrix(1457,-554,2054,-781) (19/50,8/21) -> (17/24,22/31) Glide Reflection Matrix(209,-80,546,-209) (8/21,5/13) -> (8/21,5/13) Reflection Matrix(51,-20,130,-51) (5/13,2/5) -> (5/13,2/5) Reflection Matrix(103,-42,130,-53) (2/5,5/12) -> (11/14,4/5) Hyperbolic Matrix(1611,-676,2600,-1091) (13/31,21/50) -> (13/21,31/50) Glide Reflection Matrix(519,-218,988,-415) (21/50,29/69) -> (1/2,9/17) Glide Reflection Matrix(417,-176,988,-417) (8/19,11/26) -> (8/19,11/26) Reflection Matrix(155,-66,364,-155) (11/26,3/7) -> (11/26,3/7) Reflection Matrix(2131,-924,2756,-1195) (13/30,23/53) -> (17/22,41/53) Glide Reflection Matrix(2081,-904,3354,-1457) (23/53,10/23) -> (49/79,18/29) Glide Reflection Matrix(417,-182,598,-261) (10/23,7/16) -> (16/23,7/10) Glide Reflection Matrix(209,-92,234,-103) (11/25,4/9) -> (8/9,1/1) Hyperbolic Matrix(677,-304,1040,-467) (13/29,9/20) -> (13/20,15/23) Hyperbolic Matrix(1819,-820,2886,-1301) (9/20,14/31) -> (46/73,29/46) Hyperbolic Matrix(1977,-896,2522,-1143) (19/42,5/11) -> (29/37,69/88) Hyperbolic Matrix(157,-72,338,-155) (5/11,6/13) -> (6/13,7/15) Parabolic Matrix(363,-170,442,-207) (7/15,1/2) -> (9/11,23/28) Glide Reflection Matrix(573,-304,884,-469) (9/17,8/15) -> (11/17,24/37) Glide Reflection Matrix(209,-112,390,-209) (8/15,7/13) -> (8/15,7/13) Reflection Matrix(155,-84,286,-155) (7/13,6/11) -> (7/13,6/11) Reflection Matrix(365,-202,468,-259) (11/20,5/9) -> (7/9,25/32) Hyperbolic Matrix(937,-524,1300,-727) (5/9,14/25) -> (18/25,31/43) Hyperbolic Matrix(677,-380,832,-467) (14/25,9/16) -> (13/16,22/27) Hyperbolic Matrix(209,-120,364,-209) (4/7,15/26) -> (4/7,15/26) Reflection Matrix(571,-330,988,-571) (15/26,11/19) -> (15/26,11/19) Reflection Matrix(573,-332,806,-467) (11/19,18/31) -> (22/31,5/7) Hyperbolic Matrix(519,-302,806,-469) (18/31,7/12) -> (9/14,20/31) Hyperbolic Matrix(729,-428,884,-519) (17/29,10/17) -> (14/17,19/23) Hyperbolic Matrix(521,-308,702,-415) (13/22,16/27) -> (20/27,3/4) Hyperbolic Matrix(1197,-710,1664,-987) (16/27,3/5) -> (41/57,18/25) Hyperbolic Matrix(209,-128,338,-207) (3/5,8/13) -> (8/13,13/21) Parabolic Matrix(33281,-20640,53664,-33281) (80/129,129/208) -> (80/129,129/208) Reflection Matrix(20383,-12642,32864,-20383) (129/208,49/79) -> (129/208,49/79) Reflection Matrix(989,-622,1404,-883) (5/8,17/27) -> (19/27,31/44) Hyperbolic Matrix(3641,-2294,4706,-2965) (17/27,46/73) -> (41/53,24/31) Glide Reflection Matrix(831,-524,988,-623) (29/46,12/19) -> (5/6,16/19) Glide Reflection Matrix(363,-230,494,-313) (12/19,7/11) -> (11/15,14/19) Hyperbolic Matrix(467,-298,572,-365) (7/11,16/25) -> (22/27,9/11) Hyperbolic Matrix(1249,-800,1950,-1249) (16/25,25/39) -> (16/25,25/39) Reflection Matrix(2651,-1700,4134,-2651) (25/39,34/53) -> (25/39,34/53) Reflection Matrix(1143,-734,1456,-935) (34/53,9/14) -> (40/51,11/14) Glide Reflection Matrix(625,-404,806,-521) (20/31,11/17) -> (24/31,7/9) Glide Reflection Matrix(2339,-1518,2886,-1873) (24/37,13/20) -> (47/58,30/37) Hyperbolic Matrix(781,-510,1196,-781) (15/23,17/26) -> (15/23,17/26) Reflection Matrix(103,-68,156,-103) (17/26,2/3) -> (17/26,2/3) Reflection Matrix(53,-36,78,-53) (2/3,9/13) -> (2/3,9/13) Reflection Matrix(415,-288,598,-415) (9/13,16/23) -> (9/13,16/23) Reflection Matrix(781,-548,962,-675) (7/10,26/37) -> (30/37,13/16) Hyperbolic Matrix(6709,-4730,9516,-6709) (43/61,55/78) -> (43/61,55/78) Reflection Matrix(1871,-1320,2652,-1871) (55/78,12/17) -> (55/78,12/17) Reflection Matrix(727,-514,884,-625) (12/17,17/24) -> (23/28,14/17) Hyperbolic Matrix(3223,-2318,3978,-2861) (23/32,41/57) -> (17/21,47/58) Hyperbolic Matrix(571,-412,650,-469) (31/43,13/18) -> (7/8,15/17) Hyperbolic Matrix(417,-304,572,-417) (8/11,19/26) -> (8/11,19/26) Reflection Matrix(571,-418,780,-571) (19/26,11/15) -> (19/26,11/15) Reflection Matrix(261,-200,338,-259) (3/4,10/13) -> (10/13,17/22) Parabolic Matrix(883,-690,1066,-833) (25/32,18/23) -> (24/29,5/6) Hyperbolic Matrix(209,-168,260,-209) (4/5,21/26) -> (4/5,21/26) Reflection Matrix(883,-714,1092,-883) (21/26,17/21) -> (21/26,17/21) Reflection Matrix(1977,-1634,2392,-1977) (19/23,43/52) -> (19/23,43/52) Reflection Matrix(2495,-2064,3016,-2495) (43/52,24/29) -> (43/52,24/29) Reflection Matrix(417,-352,494,-417) (16/19,11/13) -> (16/19,11/13) Reflection Matrix(155,-132,182,-155) (11/13,6/7) -> (11/13,6/7) Reflection Matrix(781,-690,884,-781) (15/17,23/26) -> (15/17,23/26) Reflection Matrix(415,-368,468,-415) (23/26,8/9) -> (23/26,8/9) Reflection Matrix(-1,2,0,1) (1/1,1/0) -> (1/1,1/0) Reflection IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,0,0,-1) -> Matrix(1,0,0,-1) (0/1,1/0) -> (0/1,1/0) Matrix(469,-40,598,-51) -> Matrix(1,-2,0,1) 1/0 Matrix(155,-16,494,-51) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(623,-74,884,-105) -> Matrix(5,-2,-2,1) Matrix(103,-14,390,-53) -> Matrix(1,0,-2,1) 0/1 Matrix(53,-8,338,-51) -> Matrix(1,-2,0,1) 1/0 Matrix(467,-74,650,-103) -> Matrix(3,4,-2,-3) *** -> (-2/1,-1/1) Matrix(157,-28,286,-51) -> Matrix(1,-2,0,1) 1/0 Matrix(365,-68,832,-155) -> Matrix(3,2,4,3) Matrix(623,-118,1378,-261) -> Matrix(5,2,2,1) Matrix(209,-40,1092,-209) -> Matrix(-1,0,8,1) (4/21,5/26) -> (-1/4,0/1) Matrix(51,-10,260,-51) -> Matrix(1,0,2,-1) (5/26,1/5) -> (0/1,1/1) Matrix(207,-44,494,-105) -> Matrix(1,0,-4,1) 0/1 Matrix(2029,-438,2886,-623) -> Matrix(5,-2,-2,1) Matrix(729,-158,1924,-417) -> Matrix(5,-2,2,-1) Matrix(209,-46,468,-103) -> Matrix(3,-2,2,-1) 1/1 Matrix(53,-12,234,-53) -> Matrix(-1,2,0,1) (2/9,3/13) -> (1/1,1/0) Matrix(103,-24,442,-103) -> Matrix(1,4,0,-1) (3/13,4/17) -> (-2/1,1/0) Matrix(261,-62,442,-105) -> Matrix(1,2,2,3) Matrix(259,-68,598,-157) -> Matrix(1,0,4,1) 0/1 Matrix(521,-138,1378,-365) -> Matrix(3,2,2,1) Matrix(209,-56,780,-209) -> Matrix(-1,0,8,1) (4/15,7/26) -> (-1/4,0/1) Matrix(155,-42,572,-155) -> Matrix(1,0,6,-1) (7/26,3/11) -> (0/1,1/3) Matrix(1039,-286,1326,-365) -> Matrix(5,-2,-2,1) Matrix(469,-130,754,-209) -> Matrix(7,-4,-2,1) Matrix(157,-44,182,-51) -> Matrix(1,-2,0,1) 1/0 Matrix(103,-30,182,-53) -> Matrix(1,0,-2,1) 0/1 Matrix(105,-32,338,-103) -> Matrix(1,-4,0,1) 1/0 Matrix(831,-262,1976,-623) -> Matrix(1,2,-6,-13) Matrix(365,-116,494,-157) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(259,-92,442,-157) -> Matrix(1,0,0,1) Matrix(1093,-392,3042,-1091) -> Matrix(5,-2,8,-3) 1/2 Matrix(2341,-842,3328,-1197) -> Matrix(7,-4,-2,1) Matrix(571,-206,1300,-469) -> Matrix(1,-2,2,-3) 1/1 Matrix(207,-76,286,-105) -> Matrix(1,-2,0,1) 1/0 Matrix(1923,-730,2600,-987) -> Matrix(3,-8,-2,5) Matrix(6449,-2450,10400,-3951) -> Matrix(31,-98,-6,19) Matrix(1457,-554,2054,-781) -> Matrix(5,-18,-2,7) Matrix(209,-80,546,-209) -> Matrix(-1,8,0,1) (8/21,5/13) -> (4/1,1/0) Matrix(51,-20,130,-51) -> Matrix(1,2,0,-1) (5/13,2/5) -> (-1/1,1/0) Matrix(103,-42,130,-53) -> Matrix(3,2,-2,-1) -1/1 Matrix(1611,-676,2600,-1091) -> Matrix(25,6,-4,-1) Matrix(519,-218,988,-415) -> Matrix(11,2,6,1) Matrix(417,-176,988,-417) -> Matrix(-1,0,16,1) (8/19,11/26) -> (-1/8,0/1) Matrix(155,-66,364,-155) -> Matrix(1,0,6,-1) (11/26,3/7) -> (0/1,1/3) Matrix(2131,-924,2756,-1195) -> Matrix(23,-6,-4,1) Matrix(2081,-904,3354,-1457) -> Matrix(37,-14,-8,3) Matrix(417,-182,598,-261) -> Matrix(11,-6,-2,1) Matrix(209,-92,234,-103) -> Matrix(3,-2,-4,3) Matrix(677,-304,1040,-467) -> Matrix(1,-2,0,1) 1/0 Matrix(1819,-820,2886,-1301) -> Matrix(1,-2,0,1) 1/0 Matrix(1977,-896,2522,-1143) -> Matrix(1,-4,0,1) 1/0 Matrix(157,-72,338,-155) -> Matrix(1,-6,0,1) 1/0 Matrix(363,-170,442,-207) -> Matrix(1,2,-2,-5) Matrix(573,-304,884,-469) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(209,-112,390,-209) -> Matrix(-1,8,0,1) (8/15,7/13) -> (4/1,1/0) Matrix(155,-84,286,-155) -> Matrix(1,6,0,-1) (7/13,6/11) -> (-3/1,1/0) Matrix(365,-202,468,-259) -> Matrix(5,8,-2,-3) -2/1 Matrix(937,-524,1300,-727) -> Matrix(5,4,-4,-3) -1/1 Matrix(677,-380,832,-467) -> Matrix(1,0,0,1) Matrix(209,-120,364,-209) -> Matrix(-1,0,4,1) (4/7,15/26) -> (-1/2,0/1) Matrix(571,-330,988,-571) -> Matrix(1,0,10,-1) (15/26,11/19) -> (0/1,1/5) Matrix(573,-332,806,-467) -> Matrix(9,-2,-4,1) Matrix(519,-302,806,-469) -> Matrix(1,0,-2,1) 0/1 Matrix(729,-428,884,-519) -> Matrix(1,0,-4,1) 0/1 Matrix(521,-308,702,-415) -> Matrix(3,-2,-4,3) Matrix(1197,-710,1664,-987) -> Matrix(3,-4,-2,3) Matrix(209,-128,338,-207) -> Matrix(1,-8,0,1) 1/0 Matrix(33281,-20640,53664,-33281) -> Matrix(141,710,-28,-141) (80/129,129/208) -> (-71/14,-5/1) Matrix(20383,-12642,32864,-20383) -> Matrix(89,440,-18,-89) (129/208,49/79) -> (-5/1,-44/9) Matrix(989,-622,1404,-883) -> Matrix(5,8,-2,-3) -2/1 Matrix(3641,-2294,4706,-2965) -> Matrix(9,4,-2,-1) Matrix(831,-524,988,-623) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(363,-230,494,-313) -> Matrix(1,2,-2,-3) -1/1 Matrix(467,-298,572,-365) -> Matrix(1,2,-2,-3) -1/1 Matrix(1249,-800,1950,-1249) -> Matrix(3,2,-4,-3) (16/25,25/39) -> (-1/1,-1/2) Matrix(2651,-1700,4134,-2651) -> Matrix(-1,0,4,1) (25/39,34/53) -> (-1/2,0/1) Matrix(1143,-734,1456,-935) -> Matrix(5,2,-2,-1) Matrix(625,-404,806,-521) -> Matrix(1,4,0,-1) *** -> (-2/1,1/0) Matrix(2339,-1518,2886,-1873) -> Matrix(5,6,-6,-7) -1/1 Matrix(781,-510,1196,-781) -> Matrix(-1,0,2,1) (15/23,17/26) -> (-1/1,0/1) Matrix(103,-68,156,-103) -> Matrix(1,0,0,-1) (17/26,2/3) -> (0/1,1/0) Matrix(53,-36,78,-53) -> Matrix(1,0,0,-1) (2/3,9/13) -> (0/1,1/0) Matrix(415,-288,598,-415) -> Matrix(1,16,0,-1) (9/13,16/23) -> (-8/1,1/0) Matrix(781,-548,962,-675) -> Matrix(3,10,-4,-13) Matrix(6709,-4730,9516,-6709) -> Matrix(13,28,-6,-13) (43/61,55/78) -> (-7/3,-2/1) Matrix(1871,-1320,2652,-1871) -> Matrix(1,4,0,-1) (55/78,12/17) -> (-2/1,1/0) Matrix(727,-514,884,-625) -> Matrix(1,2,-2,-3) -1/1 Matrix(3223,-2318,3978,-2861) -> Matrix(9,10,-10,-11) -1/1 Matrix(571,-412,650,-469) -> Matrix(5,4,-4,-3) -1/1 Matrix(417,-304,572,-417) -> Matrix(5,6,-4,-5) (8/11,19/26) -> (-3/2,-1/1) Matrix(571,-418,780,-571) -> Matrix(5,4,-6,-5) (19/26,11/15) -> (-1/1,-2/3) Matrix(261,-200,338,-259) -> Matrix(1,-6,0,1) 1/0 Matrix(883,-690,1066,-833) -> Matrix(1,2,2,5) Matrix(209,-168,260,-209) -> Matrix(5,6,-4,-5) (4/5,21/26) -> (-3/2,-1/1) Matrix(883,-714,1092,-883) -> Matrix(17,16,-18,-17) (21/26,17/21) -> (-1/1,-8/9) Matrix(1977,-1634,2392,-1977) -> Matrix(-1,0,10,1) (19/23,43/52) -> (-1/5,0/1) Matrix(2495,-2064,3016,-2495) -> Matrix(1,0,8,-1) (43/52,24/29) -> (0/1,1/4) Matrix(417,-352,494,-417) -> Matrix(-1,4,0,1) (16/19,11/13) -> (2/1,1/0) Matrix(155,-132,182,-155) -> Matrix(1,4,0,-1) (11/13,6/7) -> (-2/1,1/0) Matrix(781,-690,884,-781) -> Matrix(23,24,-22,-23) (15/17,23/26) -> (-12/11,-1/1) Matrix(415,-368,468,-415) -> Matrix(11,10,-12,-11) (23/26,8/9) -> (-1/1,-5/6) Matrix(-1,2,0,1) -> Matrix(-1,0,2,1) (1/1,1/0) -> (-1/1,0/1) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.