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): 864 Minimal number of generators: 145 Number of equivalence classes of cusps: 64 Genus: 41 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -1/1 -5/11 -7/16 -2/5 -5/14 -1/3 -1/4 -2/11 -1/7 0/1 1/5 2/7 1/3 4/11 5/13 1/2 19/35 7/11 5/7 4/5 11/13 1/1 13/11 5/4 7/5 3/2 11/7 28/17 5/3 17/10 23/13 2/1 37/17 25/11 7/3 19/8 5/2 13/5 8/3 11/4 3/1 16/5 55/17 13/4 10/3 7/2 11/3 4/1 29/7 13/3 22/5 9/2 14/3 5/1 11/2 17/3 6/1 31/5 19/3 13/2 7/1 8/1 9/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 0/1 -1/2 1/32 -6/13 2/59 3/88 -5/11 1/29 -9/20 1/28 -4/9 2/57 1/28 -11/25 1/28 -7/16 1/28 -17/39 1/28 -27/62 11/304 -10/23 1/28 2/55 -3/7 1/28 1/27 -11/26 1/27 -19/45 1/28 -8/19 2/55 1/27 -5/12 1/26 -7/17 1/26 -9/22 1/28 -2/5 0/1 2/53 -9/23 1/26 -7/18 1/28 -19/49 1/27 -12/31 0/1 1/27 -5/13 1/27 1/26 -13/34 1/27 -8/21 2/53 1/26 -3/8 1/26 -7/19 0/1 -4/11 1/26 2/51 -9/25 3/76 1/25 -5/14 1/25 -6/17 1/25 2/49 -1/3 1/24 -5/16 3/70 -4/13 1/23 -7/23 1/23 3/68 -3/10 1/22 -5/17 2/45 -2/7 2/45 1/22 -5/18 1/22 -8/29 4/87 2/43 -3/11 1/22 1/21 -7/26 1/22 -4/15 3/65 2/43 -9/34 7/150 -5/19 3/64 -1/4 1/21 -4/17 3/62 2/41 -7/30 5/102 -3/13 1/20 -2/9 2/41 1/20 -3/14 1/20 -7/33 1/20 -4/19 0/1 2/39 -1/5 1/20 1/19 -3/16 1/20 -2/11 1/19 -5/28 3/56 -8/45 2/37 1/18 -3/17 1/18 -1/6 1/18 -2/13 1/19 2/37 -3/20 1/18 -1/7 1/18 -1/8 1/16 0/1 0/1 1/16 1/7 1/15 1/14 2/13 0/1 2/27 3/19 1/12 1/6 1/16 2/11 2/29 1/14 1/5 1/14 2/9 2/27 1/13 5/22 1/13 3/13 1/14 1/13 7/30 7/90 11/47 3/38 4/17 0/1 2/25 5/21 1/12 1/4 1/14 3/11 1/14 2/7 1/13 5/17 3/38 8/27 3/38 2/25 3/10 1/12 4/13 1/13 2/25 5/16 1/13 1/3 1/13 1/12 6/17 0/1 1/12 5/14 1/12 4/11 0/1 2/25 11/30 3/38 7/19 1/12 10/27 2/25 1/12 3/8 1/12 5/13 1/12 7/18 1/12 2/5 1/12 2/23 5/12 1/12 13/31 3/37 1/12 8/19 1/12 11/26 11/130 14/33 4/47 3/35 3/7 1/12 4/9 2/23 3/34 9/20 5/56 5/11 3/34 1/11 1/2 1/11 7/13 1/12 1/11 13/24 9/100 19/35 1/11 6/11 1/11 6/65 5/9 3/32 4/7 2/21 3/31 11/19 1/10 7/12 1/10 10/17 1/10 3/5 1/11 1/10 14/23 3/32 2/21 11/18 3/32 19/31 5/52 8/13 2/21 4/41 21/34 1/10 13/21 1/10 18/29 3/31 4/41 23/37 4/41 5/8 1/10 7/11 1/10 9/14 1/10 2/3 1/10 2/19 7/10 1/10 12/17 1/10 4/39 5/7 2/19 13/18 3/28 21/29 3/28 8/11 0/1 1/9 11/15 1/10 3/4 1/10 13/17 3/28 23/30 3/28 10/13 3/28 4/37 17/22 1/9 7/9 3/28 1/9 4/5 1/9 9/11 1/9 5/44 14/17 4/35 3/26 5/6 3/26 16/19 3/26 2/17 27/32 7/60 11/13 2/17 6/7 2/17 1/8 7/8 1/9 8/9 1/9 2/17 1/1 1/8 8/7 0/1 2/15 7/6 1/8 20/17 5/38 2/15 13/11 2/15 6/5 2/15 1/7 5/4 1/7 14/11 1/7 4/27 23/18 3/20 32/25 0/1 2/13 9/7 1/7 3/20 22/17 4/27 2/13 13/10 1/6 17/13 1/7 4/3 2/13 1/6 15/11 1/6 26/19 1/6 11/8 1/6 18/13 0/1 1/6 7/5 0/1 10/7 2/15 1/7 53/37 1/7 43/30 13/90 33/23 1/7 5/34 23/16 1/7 13/9 1/6 3/2 1/6 11/7 1/6 19/12 1/6 8/5 1/6 2/11 37/23 2/11 29/18 3/16 21/13 1/6 13/8 1/5 44/27 0/1 1/4 31/19 1/4 49/30 1/0 67/41 0/1 18/11 0/1 1/8 23/14 5/32 28/17 1/6 5/3 1/6 1/5 22/13 2/11 3/16 17/10 1/5 46/27 0/1 1/6 29/17 1/6 12/7 0/1 1/5 7/4 1/4 23/13 0/1 39/22 1/14 16/9 0/1 1/9 9/5 1/6 20/11 0/1 1/6 11/6 1/6 2/1 0/1 2/11 13/6 1/6 37/17 1/6 24/11 1/6 2/11 11/5 1/6 1/5 9/4 1/4 25/11 0/1 41/18 1/12 16/7 0/1 1/8 7/3 1/6 33/14 1/6 59/25 2/11 26/11 1/6 2/11 19/8 1/5 50/21 0/1 1/4 31/13 1/6 1/5 12/5 2/11 1/5 17/7 0/1 5/2 1/6 13/5 1/5 21/8 5/24 8/3 1/5 2/9 35/13 2/9 62/23 2/9 5/22 27/10 7/30 19/7 1/4 49/18 1/2 79/29 0/1 30/11 0/1 1/6 41/15 1/5 1/4 52/19 0/1 1/4 11/4 1/5 25/9 1/4 39/14 1/4 53/19 0/1 14/5 0/1 1/5 31/11 1/5 17/6 1/4 3/1 1/5 1/4 16/5 0/1 2/9 29/9 1/4 42/13 1/5 2/9 55/17 2/9 13/4 1/4 23/7 1/4 10/3 2/9 1/4 7/2 1/4 18/5 1/4 4/15 47/13 4/15 76/21 4/15 11/41 29/8 13/48 69/19 3/11 11/40 40/11 8/29 2/7 11/3 1/4 26/7 0/1 2/7 41/11 1/4 1/3 15/4 1/4 4/1 1/4 2/7 29/7 2/7 25/6 7/24 21/5 3/10 17/4 1/3 30/7 2/7 3/10 73/17 3/10 43/10 3/10 13/3 3/10 1/3 22/5 1/3 9/2 1/4 14/3 2/7 1/3 5/1 1/3 16/3 1/3 4/11 11/2 3/8 17/3 1/3 1/2 6/1 3/8 2/5 31/5 2/5 25/4 13/32 19/3 5/12 32/5 2/5 5/12 13/2 3/7 7/1 3/7 1/2 8/1 1/2 9/1 1/2 1/0 1/0 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,2,-2,-3) (-1/1,1/0) -> (-1/1,-1/2) Parabolic Matrix(335,156,204,95) (-1/2,-6/13) -> (18/11,23/14) Hyperbolic Matrix(265,122,202,93) (-6/13,-5/11) -> (17/13,4/3) Hyperbolic Matrix(457,206,-1178,-531) (-5/11,-9/20) -> (-7/18,-19/49) Hyperbolic Matrix(325,146,394,177) (-9/20,-4/9) -> (14/17,5/6) Hyperbolic Matrix(581,256,320,141) (-4/9,-11/25) -> (9/5,20/11) Hyperbolic Matrix(447,196,-1024,-449) (-11/25,-7/16) -> (-7/16,-17/39) Parabolic Matrix(955,416,4084,1779) (-17/39,-27/62) -> (7/30,11/47) Hyperbolic Matrix(4465,1944,1656,721) (-27/62,-10/23) -> (62/23,27/10) Hyperbolic Matrix(65,28,188,81) (-10/23,-3/7) -> (1/3,6/17) Hyperbolic Matrix(61,26,190,81) (-3/7,-11/26) -> (5/16,1/3) Hyperbolic Matrix(1311,554,310,131) (-11/26,-19/45) -> (21/5,17/4) Hyperbolic Matrix(687,290,1618,683) (-19/45,-8/19) -> (14/33,3/7) Hyperbolic Matrix(495,208,188,79) (-8/19,-5/12) -> (21/8,8/3) Hyperbolic Matrix(183,76,248,103) (-5/12,-7/17) -> (11/15,3/4) Hyperbolic Matrix(185,76,-796,-327) (-7/17,-9/22) -> (-7/30,-3/13) Hyperbolic Matrix(549,224,424,173) (-9/22,-2/5) -> (22/17,13/10) Hyperbolic Matrix(653,256,176,69) (-2/5,-9/23) -> (11/3,26/7) Hyperbolic Matrix(297,116,-1124,-439) (-9/23,-7/18) -> (-9/34,-5/19) Hyperbolic Matrix(1647,638,586,227) (-19/49,-12/31) -> (14/5,31/11) Hyperbolic Matrix(1117,432,468,181) (-12/31,-5/13) -> (31/13,12/5) Hyperbolic Matrix(407,156,60,23) (-5/13,-13/34) -> (13/2,7/1) Hyperbolic Matrix(351,134,406,155) (-13/34,-8/21) -> (6/7,7/8) Hyperbolic Matrix(463,176,292,111) (-8/21,-3/8) -> (19/12,8/5) Hyperbolic Matrix(287,106,398,147) (-3/8,-7/19) -> (5/7,13/18) Hyperbolic Matrix(283,104,400,147) (-7/19,-4/11) -> (12/17,5/7) Hyperbolic Matrix(337,122,58,21) (-4/11,-9/25) -> (17/3,6/1) Hyperbolic Matrix(167,60,732,263) (-9/25,-5/14) -> (5/22,3/13) Hyperbolic Matrix(113,40,500,177) (-5/14,-6/17) -> (2/9,5/22) Hyperbolic Matrix(275,96,444,155) (-6/17,-1/3) -> (13/21,18/29) Hyperbolic Matrix(423,134,262,83) (-1/3,-5/16) -> (29/18,21/13) Hyperbolic Matrix(469,146,106,33) (-5/16,-4/13) -> (22/5,9/2) Hyperbolic Matrix(675,206,154,47) (-4/13,-7/23) -> (13/3,22/5) Hyperbolic Matrix(257,78,570,173) (-7/23,-3/10) -> (9/20,5/11) Hyperbolic Matrix(255,76,104,31) (-3/10,-5/17) -> (17/7,5/2) Hyperbolic Matrix(355,104,256,75) (-5/17,-2/7) -> (18/13,7/5) Hyperbolic Matrix(99,28,152,43) (-2/7,-5/18) -> (9/14,2/3) Hyperbolic Matrix(347,96,300,83) (-5/18,-8/29) -> (8/7,7/6) Hyperbolic Matrix(51,14,346,95) (-8/29,-3/11) -> (1/7,2/13) Hyperbolic Matrix(393,106,938,253) (-3/11,-7/26) -> (5/12,13/31) Hyperbolic Matrix(97,26,-638,-171) (-7/26,-4/15) -> (-2/13,-3/20) Hyperbolic Matrix(1129,300,636,169) (-4/15,-9/34) -> (39/22,16/9) Hyperbolic Matrix(489,128,340,89) (-5/19,-1/4) -> (23/16,13/9) Hyperbolic Matrix(329,78,426,101) (-1/4,-4/17) -> (10/13,17/22) Hyperbolic Matrix(1177,276,516,121) (-4/17,-7/30) -> (41/18,16/7) Hyperbolic Matrix(187,42,138,31) (-3/13,-2/9) -> (4/3,15/11) Hyperbolic Matrix(91,20,232,51) (-2/9,-3/14) -> (7/18,2/5) Hyperbolic Matrix(1187,252,504,107) (-3/14,-7/33) -> (7/3,33/14) Hyperbolic Matrix(227,48,960,203) (-7/33,-4/19) -> (4/17,5/21) Hyperbolic Matrix(137,28,44,9) (-4/19,-1/5) -> (3/1,16/5) Hyperbolic Matrix(133,26,46,9) (-1/5,-3/16) -> (17/6,3/1) Hyperbolic Matrix(87,16,-484,-89) (-3/16,-2/11) -> (-2/11,-5/28) Parabolic Matrix(1663,296,1972,351) (-5/28,-8/45) -> (16/19,27/32) Hyperbolic Matrix(1399,248,220,39) (-8/45,-3/17) -> (19/3,32/5) Hyperbolic Matrix(347,60,480,83) (-3/17,-1/6) -> (13/18,21/29) Hyperbolic Matrix(383,60,300,47) (-1/6,-2/13) -> (14/11,23/18) Hyperbolic Matrix(421,62,550,81) (-3/20,-1/7) -> (13/17,23/30) Hyperbolic Matrix(125,16,164,21) (-1/7,-1/8) -> (3/4,13/17) Hyperbolic Matrix(123,14,202,23) (-1/8,0/1) -> (14/23,11/18) Hyperbolic Matrix(159,-22,94,-13) (0/1,1/7) -> (5/3,22/13) Hyperbolic Matrix(219,-34,934,-145) (2/13,3/19) -> (11/47,4/17) Hyperbolic Matrix(589,-94,94,-15) (3/19,1/6) -> (25/4,19/3) Hyperbolic Matrix(123,-22,274,-49) (1/6,2/11) -> (4/9,9/20) Hyperbolic Matrix(303,-56,92,-17) (2/11,1/5) -> (23/7,10/3) Hyperbolic Matrix(119,-26,206,-45) (1/5,2/9) -> (4/7,11/19) Hyperbolic Matrix(1549,-360,1080,-251) (3/13,7/30) -> (43/30,33/23) Hyperbolic Matrix(609,-146,146,-35) (5/21,1/4) -> (25/6,21/5) Hyperbolic Matrix(85,-22,58,-15) (1/4,3/11) -> (13/9,3/2) Hyperbolic Matrix(57,-16,196,-55) (3/11,2/7) -> (2/7,5/17) Parabolic Matrix(1585,-468,972,-287) (5/17,8/27) -> (44/27,31/19) Hyperbolic Matrix(389,-116,332,-99) (8/27,3/10) -> (7/6,20/17) Hyperbolic Matrix(303,-92,56,-17) (3/10,4/13) -> (16/3,11/2) Hyperbolic Matrix(219,-68,248,-77) (4/13,5/16) -> (7/8,8/9) Hyperbolic Matrix(531,-188,692,-245) (6/17,5/14) -> (23/30,10/13) Hyperbolic Matrix(343,-124,556,-201) (5/14,4/11) -> (8/13,21/34) Hyperbolic Matrix(1213,-444,948,-347) (4/11,11/30) -> (23/18,32/25) Hyperbolic Matrix(1501,-552,552,-203) (11/30,7/19) -> (19/7,49/18) Hyperbolic Matrix(1657,-612,972,-359) (7/19,10/27) -> (46/27,29/17) Hyperbolic Matrix(263,-98,314,-117) (10/27,3/8) -> (5/6,16/19) Hyperbolic Matrix(131,-50,338,-129) (3/8,5/13) -> (5/13,7/18) Parabolic Matrix(179,-74,254,-105) (2/5,5/12) -> (7/10,12/17) Hyperbolic Matrix(963,-404,584,-245) (13/31,8/19) -> (28/17,5/3) Hyperbolic Matrix(1165,-492,708,-299) (8/19,11/26) -> (23/14,28/17) Hyperbolic Matrix(2933,-1242,810,-343) (11/26,14/33) -> (76/21,29/8) Hyperbolic Matrix(175,-76,76,-33) (3/7,4/9) -> (16/7,7/3) Hyperbolic Matrix(25,-12,48,-23) (5/11,1/2) -> (1/2,7/13) Parabolic Matrix(2033,-1100,560,-303) (7/13,13/24) -> (29/8,69/19) Hyperbolic Matrix(2777,-1506,1938,-1051) (13/24,19/35) -> (53/37,43/30) Hyperbolic Matrix(933,-508,652,-355) (19/35,6/11) -> (10/7,53/37) Hyperbolic Matrix(303,-166,418,-229) (6/11,5/9) -> (21/29,8/11) Hyperbolic Matrix(207,-116,116,-65) (5/9,4/7) -> (16/9,9/5) Hyperbolic Matrix(523,-304,160,-93) (11/19,7/12) -> (13/4,23/7) Hyperbolic Matrix(499,-292,364,-213) (7/12,10/17) -> (26/19,11/8) Hyperbolic Matrix(159,-94,22,-13) (10/17,3/5) -> (7/1,8/1) Hyperbolic Matrix(963,-584,404,-245) (3/5,14/23) -> (50/21,31/13) Hyperbolic Matrix(2077,-1272,1272,-779) (11/18,19/31) -> (31/19,49/30) Hyperbolic Matrix(1383,-848,380,-233) (19/31,8/13) -> (40/11,11/3) Hyperbolic Matrix(1669,-1032,600,-371) (21/34,13/21) -> (25/9,39/14) Hyperbolic Matrix(4175,-2594,1154,-717) (18/29,23/37) -> (47/13,76/21) Hyperbolic Matrix(1087,-676,1288,-801) (23/37,5/8) -> (27/32,11/13) Hyperbolic Matrix(155,-98,242,-153) (5/8,7/11) -> (7/11,9/14) Parabolic Matrix(85,-58,22,-15) (2/3,7/10) -> (15/4,4/1) Hyperbolic Matrix(499,-364,292,-213) (8/11,11/15) -> (29/17,12/7) Hyperbolic Matrix(933,-722,650,-503) (17/22,7/9) -> (33/23,23/16) Hyperbolic Matrix(81,-64,100,-79) (7/9,4/5) -> (4/5,9/11) Parabolic Matrix(1027,-844,376,-309) (9/11,14/17) -> (30/11,41/15) Hyperbolic Matrix(563,-480,156,-133) (11/13,6/7) -> (18/5,47/13) Hyperbolic Matrix(303,-274,94,-85) (8/9,1/1) -> (29/9,42/13) Hyperbolic Matrix(219,-248,68,-77) (1/1,8/7) -> (16/5,29/9) Hyperbolic Matrix(1289,-1518,546,-643) (20/17,13/11) -> (59/25,26/11) Hyperbolic Matrix(263,-314,98,-117) (13/11,6/5) -> (8/3,35/13) Hyperbolic Matrix(81,-100,64,-79) (6/5,5/4) -> (5/4,14/11) Parabolic Matrix(2005,-2568,552,-707) (32/25,9/7) -> (69/19,40/11) Hyperbolic Matrix(879,-1136,236,-305) (9/7,22/17) -> (26/7,41/11) Hyperbolic Matrix(531,-692,188,-245) (13/10,17/13) -> (31/11,17/6) Hyperbolic Matrix(259,-354,30,-41) (15/11,26/19) -> (8/1,9/1) Hyperbolic Matrix(303,-418,166,-229) (11/8,18/13) -> (20/11,11/6) Hyperbolic Matrix(179,-254,74,-105) (7/5,10/7) -> (12/5,17/7) Hyperbolic Matrix(155,-242,98,-153) (3/2,11/7) -> (11/7,19/12) Parabolic Matrix(1601,-2574,594,-955) (8/5,37/23) -> (35/13,62/23) Hyperbolic Matrix(1821,-2932,772,-1243) (37/23,29/18) -> (33/14,59/25) Hyperbolic Matrix(343,-556,124,-201) (21/13,13/8) -> (11/4,25/9) Hyperbolic Matrix(713,-1160,260,-423) (13/8,44/27) -> (52/19,11/4) Hyperbolic Matrix(1955,-3194,314,-513) (49/30,67/41) -> (31/5,25/4) Hyperbolic Matrix(587,-960,96,-157) (67/41,18/11) -> (6/1,31/5) Hyperbolic Matrix(681,-1156,400,-679) (22/13,17/10) -> (17/10,46/27) Parabolic Matrix(119,-206,26,-45) (12/7,7/4) -> (9/2,14/3) Hyperbolic Matrix(599,-1058,338,-597) (7/4,23/13) -> (23/13,39/22) Parabolic Matrix(25,-48,12,-23) (11/6,2/1) -> (2/1,13/6) Parabolic Matrix(1169,-2540,272,-591) (13/6,37/17) -> (73/17,43/10) Hyperbolic Matrix(1313,-2862,306,-667) (37/17,24/11) -> (30/7,73/17) Hyperbolic Matrix(711,-1556,260,-569) (24/11,11/5) -> (41/15,52/19) Hyperbolic Matrix(123,-274,22,-49) (11/5,9/4) -> (11/2,17/3) Hyperbolic Matrix(551,-1250,242,-549) (9/4,25/11) -> (25/11,41/18) Parabolic Matrix(609,-1444,256,-607) (26/11,19/8) -> (19/8,50/21) Parabolic Matrix(131,-338,50,-129) (5/2,13/5) -> (13/5,21/8) Parabolic Matrix(97,-262,10,-27) (27/10,19/7) -> (9/1,1/0) Hyperbolic Matrix(1247,-3396,300,-817) (49/18,79/29) -> (29/7,25/6) Hyperbolic Matrix(435,-1186,106,-289) (79/29,30/11) -> (4/1,29/7) Hyperbolic Matrix(1017,-2834,314,-875) (39/14,53/19) -> (55/17,13/4) Hyperbolic Matrix(1073,-2996,332,-927) (53/19,14/5) -> (42/13,55/17) Hyperbolic Matrix(57,-196,16,-55) (10/3,7/2) -> (7/2,18/5) Parabolic Matrix(525,-1958,122,-455) (41/11,15/4) -> (43/10,13/3) Hyperbolic Matrix(219,-934,34,-145) (17/4,30/7) -> (32/5,13/2) Hyperbolic Matrix(31,-150,6,-29) (14/3,5/1) -> (5/1,16/3) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,-2,-3) -> Matrix(1,0,32,1) Matrix(335,156,204,95) -> Matrix(59,-2,384,-13) Matrix(265,122,202,93) -> Matrix(117,-4,790,-27) Matrix(457,206,-1178,-531) -> Matrix(57,-2,1568,-55) Matrix(325,146,394,177) -> Matrix(59,-2,502,-17) Matrix(581,256,320,141) -> Matrix(57,-2,314,-11) Matrix(447,196,-1024,-449) -> Matrix(169,-6,4704,-167) Matrix(955,416,4084,1779) -> Matrix(277,-10,3518,-127) Matrix(4465,1944,1656,721) -> Matrix(331,-12,1462,-53) Matrix(65,28,188,81) -> Matrix(55,-2,688,-25) Matrix(61,26,190,81) -> Matrix(55,-2,688,-25) Matrix(1311,554,310,131) -> Matrix(53,-2,186,-7) Matrix(687,290,1618,683) -> Matrix(57,-2,656,-23) Matrix(495,208,188,79) -> Matrix(109,-4,518,-19) Matrix(183,76,248,103) -> Matrix(53,-2,504,-19) Matrix(185,76,-796,-327) -> Matrix(51,-2,1046,-41) Matrix(549,224,424,173) -> Matrix(55,-2,358,-13) Matrix(653,256,176,69) -> Matrix(53,-2,186,-7) Matrix(297,116,-1124,-439) -> Matrix(49,-2,1054,-43) Matrix(1647,638,586,227) -> Matrix(1,0,-22,1) Matrix(1117,432,468,181) -> Matrix(53,-2,292,-11) Matrix(407,156,60,23) -> Matrix(51,-2,128,-5) Matrix(351,134,406,155) -> Matrix(1,0,-18,1) Matrix(463,176,292,111) -> Matrix(105,-4,604,-23) Matrix(287,106,398,147) -> Matrix(49,-2,466,-19) Matrix(283,104,400,147) -> Matrix(53,-2,504,-19) Matrix(337,122,58,21) -> Matrix(101,-4,278,-11) Matrix(167,60,732,263) -> Matrix(51,-2,638,-25) Matrix(113,40,500,177) -> Matrix(99,-4,1312,-53) Matrix(275,96,444,155) -> Matrix(47,-2,494,-21) Matrix(423,134,262,83) -> Matrix(1,0,-18,1) Matrix(469,146,106,33) -> Matrix(47,-2,118,-5) Matrix(675,206,154,47) -> Matrix(137,-6,434,-19) Matrix(257,78,570,173) -> Matrix(137,-6,1530,-67) Matrix(255,76,104,31) -> Matrix(45,-2,248,-11) Matrix(355,104,256,75) -> Matrix(45,-2,248,-11) Matrix(99,28,152,43) -> Matrix(89,-4,868,-39) Matrix(347,96,300,83) -> Matrix(43,-2,366,-17) Matrix(51,14,346,95) -> Matrix(43,-2,624,-29) Matrix(393,106,938,253) -> Matrix(87,-4,1066,-49) Matrix(97,26,-638,-171) -> Matrix(87,-4,1588,-73) Matrix(1129,300,636,169) -> Matrix(43,-2,452,-21) Matrix(489,128,340,89) -> Matrix(85,-4,574,-27) Matrix(329,78,426,101) -> Matrix(125,-6,1146,-55) Matrix(1177,276,516,121) -> Matrix(41,-2,390,-19) Matrix(187,42,138,31) -> Matrix(1,0,-14,1) Matrix(91,20,232,51) -> Matrix(81,-4,952,-47) Matrix(1187,252,504,107) -> Matrix(1,0,-14,1) Matrix(227,48,960,203) -> Matrix(39,-2,488,-25) Matrix(137,28,44,9) -> Matrix(39,-2,176,-9) Matrix(133,26,46,9) -> Matrix(39,-2,176,-9) Matrix(87,16,-484,-89) -> Matrix(77,-4,1444,-75) Matrix(1663,296,1972,351) -> Matrix(147,-8,1268,-69) Matrix(1399,248,220,39) -> Matrix(149,-8,354,-19) Matrix(347,60,480,83) -> Matrix(75,-4,694,-37) Matrix(383,60,300,47) -> Matrix(39,-2,254,-13) Matrix(421,62,550,81) -> Matrix(75,-4,694,-37) Matrix(125,16,164,21) -> Matrix(33,-2,314,-19) Matrix(123,14,202,23) -> Matrix(35,-2,368,-21) Matrix(159,-22,94,-13) -> Matrix(29,-2,160,-11) Matrix(219,-34,934,-145) -> Matrix(27,-2,338,-25) Matrix(589,-94,94,-15) -> Matrix(19,-2,48,-5) Matrix(123,-22,274,-49) -> Matrix(59,-4,664,-45) Matrix(303,-56,92,-17) -> Matrix(1,0,-10,1) Matrix(119,-26,206,-45) -> Matrix(55,-4,564,-41) Matrix(1549,-360,1080,-251) -> Matrix(79,-6,540,-41) Matrix(609,-146,146,-35) -> Matrix(21,-2,74,-7) Matrix(85,-22,58,-15) -> Matrix(27,-2,176,-13) Matrix(57,-16,196,-55) -> Matrix(53,-4,676,-51) Matrix(1585,-468,972,-287) -> Matrix(25,-2,138,-11) Matrix(389,-116,332,-99) -> Matrix(49,-4,380,-31) Matrix(303,-92,56,-17) -> Matrix(27,-2,68,-5) Matrix(219,-68,248,-77) -> Matrix(1,0,-4,1) Matrix(531,-188,692,-245) -> Matrix(51,-4,472,-37) Matrix(343,-124,556,-201) -> Matrix(23,-2,242,-21) Matrix(1213,-444,948,-347) -> Matrix(1,0,-6,1) Matrix(1501,-552,552,-203) -> Matrix(25,-2,88,-7) Matrix(1657,-612,972,-359) -> Matrix(25,-2,138,-11) Matrix(263,-98,314,-117) -> Matrix(99,-8,854,-69) Matrix(131,-50,338,-129) -> Matrix(121,-10,1440,-119) Matrix(179,-74,254,-105) -> Matrix(25,-2,238,-19) Matrix(963,-404,584,-245) -> Matrix(49,-4,282,-23) Matrix(1165,-492,708,-299) -> Matrix(95,-8,582,-49) Matrix(2933,-1242,810,-343) -> Matrix(377,-32,1402,-119) Matrix(175,-76,76,-33) -> Matrix(23,-2,150,-13) Matrix(25,-12,48,-23) -> Matrix(23,-2,242,-21) Matrix(2033,-1100,560,-303) -> Matrix(157,-14,572,-51) Matrix(2777,-1506,1938,-1051) -> Matrix(243,-22,1690,-153) Matrix(933,-508,652,-355) -> Matrix(87,-8,620,-57) Matrix(303,-166,418,-229) -> Matrix(65,-6,596,-55) Matrix(207,-116,116,-65) -> Matrix(21,-2,158,-15) Matrix(523,-304,160,-93) -> Matrix(21,-2,74,-7) Matrix(499,-292,364,-213) -> Matrix(41,-4,236,-23) Matrix(159,-94,22,-13) -> Matrix(19,-2,48,-5) Matrix(963,-584,404,-245) -> Matrix(21,-2,116,-11) Matrix(2077,-1272,1272,-779) -> Matrix(21,-2,32,-3) Matrix(1383,-848,380,-233) -> Matrix(125,-12,448,-43) Matrix(1669,-1032,600,-371) -> Matrix(21,-2,74,-7) Matrix(4175,-2594,1154,-717) -> Matrix(575,-56,2146,-209) Matrix(1087,-676,1288,-801) -> Matrix(307,-30,2630,-257) Matrix(155,-98,242,-153) -> Matrix(141,-14,1400,-139) Matrix(85,-58,22,-15) -> Matrix(1,0,-6,1) Matrix(499,-364,292,-213) -> Matrix(1,0,-4,1) Matrix(933,-722,650,-503) -> Matrix(73,-8,502,-55) Matrix(81,-64,100,-79) -> Matrix(73,-8,648,-71) Matrix(1027,-844,376,-309) -> Matrix(35,-4,184,-21) Matrix(563,-480,156,-133) -> Matrix(49,-6,188,-23) Matrix(303,-274,94,-85) -> Matrix(1,0,-4,1) Matrix(219,-248,68,-77) -> Matrix(15,-2,68,-9) Matrix(1289,-1518,546,-643) -> Matrix(61,-8,328,-43) Matrix(263,-314,98,-117) -> Matrix(29,-4,138,-19) Matrix(81,-100,64,-79) -> Matrix(43,-6,294,-41) Matrix(2005,-2568,552,-707) -> Matrix(17,-2,60,-7) Matrix(879,-1136,236,-305) -> Matrix(27,-4,88,-13) Matrix(531,-692,188,-245) -> Matrix(1,0,-2,1) Matrix(259,-354,30,-41) -> Matrix(37,-6,68,-11) Matrix(303,-418,166,-229) -> Matrix(1,0,0,1) Matrix(179,-254,74,-105) -> Matrix(1,0,-2,1) Matrix(155,-242,98,-153) -> Matrix(37,-6,216,-35) Matrix(1601,-2574,594,-955) -> Matrix(67,-12,296,-53) Matrix(1821,-2932,772,-1243) -> Matrix(43,-8,242,-45) Matrix(343,-556,124,-201) -> Matrix(11,-2,50,-9) Matrix(713,-1160,260,-423) -> Matrix(1,0,0,1) Matrix(1955,-3194,314,-513) -> Matrix(13,2,32,5) Matrix(587,-960,96,-157) -> Matrix(19,-2,48,-5) Matrix(681,-1156,400,-679) -> Matrix(11,-2,50,-9) Matrix(119,-206,26,-45) -> Matrix(9,-2,32,-7) Matrix(599,-1058,338,-597) -> Matrix(1,0,10,1) Matrix(25,-48,12,-23) -> Matrix(1,0,0,1) Matrix(1169,-2540,272,-591) -> Matrix(9,-2,32,-7) Matrix(1313,-2862,306,-667) -> Matrix(45,-8,152,-27) Matrix(711,-1556,260,-569) -> Matrix(11,-2,50,-9) Matrix(123,-274,22,-49) -> Matrix(11,-2,28,-5) Matrix(551,-1250,242,-549) -> Matrix(1,0,8,1) Matrix(609,-1444,256,-607) -> Matrix(11,-2,50,-9) Matrix(131,-338,50,-129) -> Matrix(31,-6,150,-29) Matrix(97,-262,10,-27) -> Matrix(17,-4,30,-7) Matrix(1247,-3396,300,-817) -> Matrix(3,2,10,7) Matrix(435,-1186,106,-289) -> Matrix(13,-2,46,-7) Matrix(1017,-2834,314,-875) -> Matrix(7,-2,32,-9) Matrix(1073,-2996,332,-927) -> Matrix(11,-2,50,-9) Matrix(57,-196,16,-55) -> Matrix(25,-6,96,-23) Matrix(525,-1958,122,-455) -> Matrix(5,-2,18,-7) Matrix(219,-934,34,-145) -> Matrix(15,-4,34,-9) Matrix(31,-150,6,-29) -> Matrix(19,-6,54,-17) 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): 48 Degree of the the map X: 48 Degree of the the map Y: 144 ----------------------------------------------------------------------- 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 -1/1 0/1 16 1 0/1 (0/1,1/16) 0 18 1/7 0 9 1/6 1/16 1 18 2/11 (2/29,1/14) 0 18 1/5 1/14 1 3 2/9 (2/27,1/13) 0 18 3/13 0 9 7/30 7/90 1 18 4/17 0 6 1/4 1/14 1 18 3/11 1/14 1 9 2/7 1/13 2 2 5/17 3/38 1 9 8/27 (3/38,2/25) 0 18 3/10 1/12 1 18 4/13 (1/13,2/25) 0 18 1/3 0 9 5/14 1/12 1 18 4/11 0 6 11/30 3/38 1 18 7/19 1/12 1 9 10/27 (2/25,1/12) 0 18 3/8 1/12 1 18 5/13 1/12 5 1 2/5 (1/12,2/23) 0 18 5/12 1/12 1 18 8/19 1/12 6 2 11/26 11/130 1 18 3/7 1/12 1 9 4/9 (2/23,3/34) 0 18 5/11 0 9 1/2 1/11 1 6 7/13 0 9 13/24 9/100 1 18 19/35 1/11 15 1 6/11 (1/11,6/65) 0 18 5/9 3/32 1 9 4/7 (2/21,3/31) 0 18 11/19 1/10 1 3 7/12 1/10 1 18 10/17 1/10 6 2 3/5 0 9 11/18 3/32 1 18 19/31 5/52 1 9 8/13 0 6 21/34 1/10 1 18 13/21 1/10 1 9 5/8 1/10 1 18 7/11 1/10 7 1 2/3 (1/10,2/19) 0 18 7/10 1/10 1 18 5/7 2/19 1 3 8/11 (0/1,1/9) 0 18 3/4 1/10 1 18 10/13 (3/28,4/37) 0 18 7/9 0 9 4/5 1/9 4 2 9/11 0 9 5/6 3/26 1 18 16/19 (3/26,2/17) 0 18 11/13 2/17 4 3 6/7 (2/17,1/8) 0 18 1/1 1/8 1 9 7/6 1/8 1 18 20/17 (5/38,2/15) 0 18 13/11 2/15 4 3 6/5 (2/15,1/7) 0 18 5/4 1/7 3 2 14/11 (1/7,4/27) 0 18 9/7 0 9 13/10 1/6 1 18 4/3 (2/13,1/6) 0 18 11/8 1/6 1 18 7/5 0/1 1 3 10/7 (2/15,1/7) 0 18 13/9 1/6 1 9 3/2 1/6 1 18 11/7 1/6 3 1 8/5 (1/6,2/11) 0 18 21/13 1/6 1 9 13/8 1/5 1 6 44/27 (0/1,1/4) 0 18 31/19 1/4 1 9 49/30 1/0 1 18 67/41 0/1 8 1 18/11 (0/1,1/8) 0 18 5/3 0 9 22/13 (2/11,3/16) 0 18 17/10 1/5 1 2 12/7 (0/1,1/5) 0 18 7/4 1/4 1 18 23/13 0/1 5 1 16/9 (0/1,1/9) 0 18 9/5 1/6 1 9 11/6 1/6 1 18 2/1 0 6 13/6 1/6 1 18 37/17 1/6 1 1 24/11 (1/6,2/11) 0 18 11/5 0 9 9/4 1/4 1 18 25/11 0/1 4 1 16/7 (0/1,1/8) 0 18 7/3 1/6 1 9 26/11 (1/6,2/11) 0 18 19/8 1/5 1 2 12/5 (2/11,1/5) 0 18 5/2 1/6 1 18 13/5 1/5 3 1 8/3 (1/5,2/9) 0 18 35/13 2/9 4 3 27/10 7/30 1 18 19/7 1/4 1 9 49/18 1/2 1 18 79/29 0/1 4 1 30/11 (0/1,1/6) 0 18 11/4 1/5 1 6 25/9 1/4 1 9 39/14 1/4 1 18 53/19 0/1 1 1 14/5 (0/1,1/5) 0 18 3/1 0 9 13/4 1/4 1 18 23/7 1/4 1 3 10/3 (2/9,1/4) 0 18 7/2 1/4 3 2 18/5 (1/4,4/15) 0 18 47/13 4/15 4 3 29/8 13/48 1 18 40/11 0 6 11/3 1/4 1 9 15/4 1/4 1 18 4/1 (1/4,2/7) 0 18 17/4 1/3 1 6 30/7 (2/7,3/10) 0 18 13/3 0 9 9/2 1/4 1 18 14/3 (2/7,1/3) 0 18 5/1 1/3 3 3 16/3 (1/3,4/11) 0 18 11/2 3/8 1 18 6/1 (3/8,2/5) 0 18 7/1 0 9 8/1 1/2 6 2 1/0 1/0 1 18 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,2,0,-1) (-1/1,1/0) -> (-1/1,1/0) Reflection Matrix(-1,0,2,1) (-1/1,0/1) -> (-1/1,0/1) Reflection Matrix(159,-22,94,-13) (0/1,1/7) -> (5/3,22/13) Hyperbolic Matrix(95,-14,156,-23) (1/7,1/6) -> (3/5,11/18) Glide Reflection Matrix(93,-16,122,-21) (1/6,2/11) -> (3/4,10/13) Glide Reflection Matrix(303,-56,92,-17) (2/11,1/5) -> (23/7,10/3) Hyperbolic Matrix(119,-26,206,-45) (1/5,2/9) -> (4/7,11/19) Hyperbolic Matrix(263,-60,206,-47) (2/9,3/13) -> (14/11,9/7) Glide Reflection Matrix(379,-88,702,-163) (3/13,7/30) -> (7/13,13/24) Glide Reflection Matrix(1693,-396,466,-109) (7/30,4/17) -> (29/8,40/11) Glide Reflection Matrix(203,-48,554,-131) (4/17,1/4) -> (4/11,11/30) Glide Reflection Matrix(85,-22,58,-15) (1/4,3/11) -> (13/9,3/2) Hyperbolic Matrix(57,-16,196,-55) (3/11,2/7) -> (2/7,5/17) Parabolic Matrix(1585,-468,972,-287) (5/17,8/27) -> (44/27,31/19) Hyperbolic Matrix(389,-116,332,-99) (8/27,3/10) -> (7/6,20/17) Hyperbolic Matrix(303,-92,56,-17) (3/10,4/13) -> (16/3,11/2) Hyperbolic Matrix(81,-26,28,-9) (4/13,1/3) -> (14/5,3/1) Glide Reflection Matrix(81,-28,26,-9) (1/3,5/14) -> (3/1,13/4) Glide Reflection Matrix(343,-124,556,-201) (5/14,4/11) -> (8/13,21/34) Hyperbolic Matrix(1501,-552,552,-203) (11/30,7/19) -> (19/7,49/18) Hyperbolic Matrix(683,-252,290,-107) (7/19,10/27) -> (7/3,26/11) Glide Reflection Matrix(263,-98,314,-117) (10/27,3/8) -> (5/6,16/19) Hyperbolic Matrix(79,-30,208,-79) (3/8,5/13) -> (3/8,5/13) Reflection Matrix(51,-20,130,-51) (5/13,2/5) -> (5/13,2/5) Reflection Matrix(103,-42,76,-31) (2/5,5/12) -> (4/3,11/8) Glide Reflection Matrix(253,-106,432,-181) (5/12,8/19) -> (7/12,10/17) Glide Reflection Matrix(227,-96,26,-11) (8/19,11/26) -> (8/1,1/0) Glide Reflection Matrix(683,-290,252,-107) (11/26,3/7) -> (27/10,19/7) Glide Reflection Matrix(175,-76,76,-33) (3/7,4/9) -> (16/7,7/3) Hyperbolic Matrix(173,-78,224,-101) (4/9,5/11) -> (10/13,7/9) Glide Reflection Matrix(25,-12,48,-23) (5/11,1/2) -> (1/2,7/13) Parabolic Matrix(911,-494,1680,-911) (13/24,19/35) -> (13/24,19/35) Reflection Matrix(419,-228,770,-419) (19/35,6/11) -> (19/35,6/11) Reflection Matrix(233,-128,162,-89) (6/11,5/9) -> (10/7,13/9) Glide Reflection Matrix(207,-116,116,-65) (5/9,4/7) -> (16/9,9/5) Hyperbolic Matrix(523,-304,160,-93) (11/19,7/12) -> (13/4,23/7) Hyperbolic Matrix(159,-94,22,-13) (10/17,3/5) -> (7/1,8/1) Hyperbolic Matrix(2077,-1272,1272,-779) (11/18,19/31) -> (31/19,49/30) Hyperbolic Matrix(1383,-848,380,-233) (19/31,8/13) -> (40/11,11/3) Hyperbolic Matrix(1669,-1032,600,-371) (21/34,13/21) -> (25/9,39/14) Hyperbolic Matrix(155,-96,134,-83) (13/21,5/8) -> (1/1,7/6) Glide Reflection Matrix(111,-70,176,-111) (5/8,7/11) -> (5/8,7/11) Reflection Matrix(43,-28,66,-43) (7/11,2/3) -> (7/11,2/3) Reflection Matrix(85,-58,22,-15) (2/3,7/10) -> (15/4,4/1) Hyperbolic Matrix(147,-104,106,-75) (7/10,5/7) -> (11/8,7/5) Glide Reflection Matrix(147,-106,104,-75) (5/7,8/11) -> (7/5,10/7) Glide Reflection Matrix(103,-76,42,-31) (8/11,3/4) -> (12/5,5/2) Glide Reflection Matrix(81,-64,100,-79) (7/9,4/5) -> (4/5,9/11) Parabolic Matrix(177,-146,40,-33) (9/11,5/6) -> (13/3,9/2) Glide Reflection Matrix(507,-428,430,-363) (16/19,11/13) -> (20/17,13/11) Glide Reflection Matrix(563,-480,156,-133) (11/13,6/7) -> (18/5,47/13) Hyperbolic Matrix(155,-134,96,-83) (6/7,1/1) -> (8/5,21/13) Glide Reflection Matrix(263,-314,98,-117) (13/11,6/5) -> (8/3,35/13) Hyperbolic Matrix(81,-100,64,-79) (6/5,5/4) -> (5/4,14/11) Parabolic Matrix(173,-224,78,-101) (9/7,13/10) -> (11/5,9/4) Glide Reflection Matrix(93,-122,16,-21) (13/10,4/3) -> (11/2,6/1) Glide Reflection Matrix(43,-66,28,-43) (3/2,11/7) -> (3/2,11/7) Reflection Matrix(111,-176,70,-111) (11/7,8/5) -> (11/7,8/5) Reflection Matrix(343,-556,124,-201) (21/13,13/8) -> (11/4,25/9) Hyperbolic Matrix(699,-1138,164,-267) (13/8,44/27) -> (17/4,30/7) Glide Reflection Matrix(4019,-6566,2460,-4019) (49/30,67/41) -> (49/30,67/41) Reflection Matrix(1475,-2412,902,-1475) (67/41,18/11) -> (67/41,18/11) Reflection Matrix(95,-156,14,-23) (18/11,5/3) -> (6/1,7/1) Glide Reflection Matrix(507,-860,214,-363) (22/13,17/10) -> (26/11,19/8) Glide Reflection Matrix(253,-432,106,-181) (17/10,12/7) -> (19/8,12/5) Glide Reflection Matrix(119,-206,26,-45) (12/7,7/4) -> (9/2,14/3) Hyperbolic Matrix(183,-322,104,-183) (7/4,23/13) -> (7/4,23/13) Reflection Matrix(415,-736,234,-415) (23/13,16/9) -> (23/13,16/9) Reflection Matrix(141,-256,38,-69) (9/5,11/6) -> (11/3,15/4) Glide Reflection Matrix(25,-48,12,-23) (11/6,2/1) -> (2/1,13/6) Parabolic Matrix(443,-962,204,-443) (13/6,37/17) -> (13/6,37/17) Reflection Matrix(815,-1776,374,-815) (37/17,24/11) -> (37/17,24/11) Reflection Matrix(293,-642,68,-149) (24/11,11/5) -> (30/7,13/3) Glide Reflection Matrix(199,-450,88,-199) (9/4,25/11) -> (9/4,25/11) Reflection Matrix(351,-800,154,-351) (25/11,16/7) -> (25/11,16/7) Reflection Matrix(51,-130,20,-51) (5/2,13/5) -> (5/2,13/5) Reflection Matrix(79,-208,30,-79) (13/5,8/3) -> (13/5,8/3) Reflection Matrix(847,-2284,234,-631) (35/13,27/10) -> (47/13,29/8) Glide Reflection Matrix(2843,-7742,1044,-2843) (49/18,79/29) -> (49/18,79/29) Reflection Matrix(1739,-4740,638,-1739) (79/29,30/11) -> (79/29,30/11) Reflection Matrix(203,-554,48,-131) (30/11,11/4) -> (4/1,17/4) Glide Reflection Matrix(1483,-4134,532,-1483) (39/14,53/19) -> (39/14,53/19) Reflection Matrix(531,-1484,190,-531) (53/19,14/5) -> (53/19,14/5) Reflection Matrix(57,-196,16,-55) (10/3,7/2) -> (7/2,18/5) Parabolic Matrix(31,-150,6,-29) (14/3,5/1) -> (5/1,16/3) Parabolic IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,2,0,-1) -> Matrix(1,0,0,-1) (-1/1,1/0) -> (0/1,1/0) Matrix(-1,0,2,1) -> Matrix(1,0,32,-1) (-1/1,0/1) -> (0/1,1/16) Matrix(159,-22,94,-13) -> Matrix(29,-2,160,-11) Matrix(95,-14,156,-23) -> Matrix(29,-2,304,-21) Matrix(93,-16,122,-21) -> Matrix(31,-2,294,-19) Matrix(303,-56,92,-17) -> Matrix(1,0,-10,1) 0/1 Matrix(119,-26,206,-45) -> Matrix(55,-4,564,-41) Matrix(263,-60,206,-47) -> Matrix(25,-2,162,-13) Matrix(379,-88,702,-163) -> Matrix(27,-2,310,-23) Matrix(1693,-396,466,-109) -> Matrix(101,-8,366,-29) Matrix(203,-48,554,-131) -> Matrix(25,-2,312,-25) *** -> (1/13,1/12) Matrix(85,-22,58,-15) -> Matrix(27,-2,176,-13) Matrix(57,-16,196,-55) -> Matrix(53,-4,676,-51) 1/13 Matrix(1585,-468,972,-287) -> Matrix(25,-2,138,-11) Matrix(389,-116,332,-99) -> Matrix(49,-4,380,-31) Matrix(303,-92,56,-17) -> Matrix(27,-2,68,-5) Matrix(81,-26,28,-9) -> Matrix(25,-2,112,-9) Matrix(81,-28,26,-9) -> Matrix(25,-2,112,-9) Matrix(343,-124,556,-201) -> Matrix(23,-2,242,-21) 1/11 Matrix(1501,-552,552,-203) -> Matrix(25,-2,88,-7) Matrix(683,-252,290,-107) -> Matrix(1,0,18,-1) *** -> (0/1,1/9) Matrix(263,-98,314,-117) -> Matrix(99,-8,854,-69) Matrix(79,-30,208,-79) -> Matrix(73,-6,888,-73) (3/8,5/13) -> (3/37,1/12) Matrix(51,-20,130,-51) -> Matrix(47,-4,552,-47) (5/13,2/5) -> (1/12,2/23) Matrix(103,-42,76,-31) -> Matrix(1,0,18,-1) *** -> (0/1,1/9) Matrix(253,-106,432,-181) -> Matrix(49,-4,502,-41) Matrix(227,-96,26,-11) -> Matrix(71,-6,130,-11) Matrix(683,-290,252,-107) -> Matrix(23,-2,80,-7) Matrix(175,-76,76,-33) -> Matrix(23,-2,150,-13) Matrix(173,-78,224,-101) -> Matrix(67,-6,614,-55) Matrix(25,-12,48,-23) -> Matrix(23,-2,242,-21) 1/11 Matrix(911,-494,1680,-911) -> Matrix(199,-18,2200,-199) (13/24,19/35) -> (9/100,1/11) Matrix(419,-228,770,-419) -> Matrix(131,-12,1430,-131) (19/35,6/11) -> (1/11,6/65) Matrix(233,-128,162,-89) -> Matrix(43,-4,290,-27) Matrix(207,-116,116,-65) -> Matrix(21,-2,158,-15) Matrix(523,-304,160,-93) -> Matrix(21,-2,74,-7) Matrix(159,-94,22,-13) -> Matrix(19,-2,48,-5) Matrix(2077,-1272,1272,-779) -> Matrix(21,-2,32,-3) Matrix(1383,-848,380,-233) -> Matrix(125,-12,448,-43) Matrix(1669,-1032,600,-371) -> Matrix(21,-2,74,-7) Matrix(155,-96,134,-83) -> Matrix(21,-2,178,-17) Matrix(111,-70,176,-111) -> Matrix(101,-10,1020,-101) (5/8,7/11) -> (5/51,1/10) Matrix(43,-28,66,-43) -> Matrix(39,-4,380,-39) (7/11,2/3) -> (1/10,2/19) Matrix(85,-58,22,-15) -> Matrix(1,0,-6,1) 0/1 Matrix(147,-104,106,-75) -> Matrix(19,-2,104,-11) Matrix(147,-106,104,-75) -> Matrix(19,-2,142,-15) Matrix(103,-76,42,-31) -> Matrix(19,-2,104,-11) Matrix(81,-64,100,-79) -> Matrix(73,-8,648,-71) 1/9 Matrix(177,-146,40,-33) -> Matrix(17,-2,42,-5) Matrix(507,-428,430,-363) -> Matrix(137,-16,1036,-121) Matrix(563,-480,156,-133) -> Matrix(49,-6,188,-23) Matrix(155,-134,96,-83) -> Matrix(1,0,14,-1) *** -> (0/1,1/7) Matrix(263,-314,98,-117) -> Matrix(29,-4,138,-19) Matrix(81,-100,64,-79) -> Matrix(43,-6,294,-41) 1/7 Matrix(173,-224,78,-101) -> Matrix(13,-2,58,-9) Matrix(93,-122,16,-21) -> Matrix(27,-4,74,-11) Matrix(43,-66,28,-43) -> Matrix(13,-2,84,-13) (3/2,11/7) -> (1/7,1/6) Matrix(111,-176,70,-111) -> Matrix(23,-4,132,-23) (11/7,8/5) -> (1/6,2/11) Matrix(343,-556,124,-201) -> Matrix(11,-2,50,-9) 1/5 Matrix(699,-1138,164,-267) -> Matrix(11,-2,38,-7) Matrix(4019,-6566,2460,-4019) -> Matrix(1,0,0,-1) (49/30,67/41) -> (0/1,1/0) Matrix(1475,-2412,902,-1475) -> Matrix(1,0,16,-1) (67/41,18/11) -> (0/1,1/8) Matrix(95,-156,14,-23) -> Matrix(13,-2,32,-5) Matrix(507,-860,214,-363) -> Matrix(21,-4,110,-21) *** -> (2/11,1/5) Matrix(253,-432,106,-181) -> Matrix(11,-2,60,-11) *** -> (1/6,1/5) Matrix(119,-206,26,-45) -> Matrix(9,-2,32,-7) 1/4 Matrix(183,-322,104,-183) -> Matrix(1,0,8,-1) (7/4,23/13) -> (0/1,1/4) Matrix(415,-736,234,-415) -> Matrix(1,0,18,-1) (23/13,16/9) -> (0/1,1/9) Matrix(141,-256,38,-69) -> Matrix(11,-2,38,-7) Matrix(25,-48,12,-23) -> Matrix(1,0,0,1) Matrix(443,-962,204,-443) -> Matrix(11,-2,60,-11) (13/6,37/17) -> (1/6,1/5) Matrix(815,-1776,374,-815) -> Matrix(23,-4,132,-23) (37/17,24/11) -> (1/6,2/11) Matrix(293,-642,68,-149) -> Matrix(21,-4,68,-13) Matrix(199,-450,88,-199) -> Matrix(1,0,8,-1) (9/4,25/11) -> (0/1,1/4) Matrix(351,-800,154,-351) -> Matrix(1,0,16,-1) (25/11,16/7) -> (0/1,1/8) Matrix(51,-130,20,-51) -> Matrix(11,-2,60,-11) (5/2,13/5) -> (1/6,1/5) Matrix(79,-208,30,-79) -> Matrix(19,-4,90,-19) (13/5,8/3) -> (1/5,2/9) Matrix(847,-2284,234,-631) -> Matrix(79,-18,294,-67) Matrix(2843,-7742,1044,-2843) -> Matrix(1,0,4,-1) (49/18,79/29) -> (0/1,1/2) Matrix(1739,-4740,638,-1739) -> Matrix(1,0,12,-1) (79/29,30/11) -> (0/1,1/6) Matrix(203,-554,48,-131) -> Matrix(11,-2,38,-7) Matrix(1483,-4134,532,-1483) -> Matrix(1,0,8,-1) (39/14,53/19) -> (0/1,1/4) Matrix(531,-1484,190,-531) -> Matrix(1,0,10,-1) (53/19,14/5) -> (0/1,1/5) Matrix(57,-196,16,-55) -> Matrix(25,-6,96,-23) 1/4 Matrix(31,-150,6,-29) -> Matrix(19,-6,54,-17) 1/3 ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.