pgr31:=function()
local f,g,sg,s;
f:=FreeGroup("a","b","c","d","e");
g:=f/[f.1^2,f.2^2,f.3^2,f.4^2,f.5^2,f.3*f.4*f.3*f.4,f.1*f.5*f.1*f.5,f.4*f.5*f.4*f.5,f.1*f.3*f.2*f.1*f.2*f.3,f.1*f.3*f.2*f.3*f.1*f.2,f.1*f.4*f.1*f.4*f.1*f.4,f.2*f.4*f.2*f.4*f.2*f.4,f.2*f.5*f.2*f.5*f.2*f.5,f.5*f.3*f.5*f.3*f.5*f.3];
sg:=Subgroup(g,[g.1,g.2*g.3,g.4]);
s:=Image(ActionHomomorphism(g,RightTransversal(g,sg),OnRight));
return s;
end;
G31:=pgr31(); gap> Size(G31); 46080 gap> N31:=NormalSubgroups(G31);; gap> NTSize(N31); Groesse des 1. Normalteilers: 1 Groesse des 2. Normalteilers: 2 Groesse des 3. Normalteilers: 4 Groesse des 4. Normalteilers: 64 Groesse des 5. Normalteilers: 23040 Groesse des 6. Normalteilers: 46080 gap> Centre(G31); <permutation group of size 4 with 2 generators> gap> Size(Centre(G31)); 4 gap> IsSolvable(G31); false gap> CompositionSeries(G31); [ <permutation group of size 46080 with 9 generators>, <permutation group of size 23040 with 8 generators>, <permutation group of size 64 with 7 generators>, <permutation group of size 32 with 4 generators>, <permutation group of size 16 with 4 generators>, <permutation group of size 8 with 3 generators>, <permutation group of size 4 with 2 generators>, <permutation group of size 2 with 1 generators>, Group(()) ]
gap> ct31:=CharacterTable(G31); CharacterTable( <permutation group of size 46080 with 5 generators> ) gap> Display(ct31); CT1 2 10 10 9 9 10 10 8 8 6 8 8 3 3 3 3 8 8 8 8 5 7 3 2 2 1 1 2 2 1 1 . 1 1 2 2 2 2 . . . . . . 5 1 1 . . 1 1 . . . . . . . . . . . . . . . 1a 2a 2b 4a 4b 4c 2c 2d 4d 4e 4f 12a 12b 3a 6a 4g 4h 4i 4j 8a 2e 2P 1a 1a 1a 2a 2a 2a 1a 1a 2b 2a 2a 6a 6a 3a 3a 2b 2b 2b 2b 4a 1a 3P 1a 2a 2b 4a 4c 4b 2c 2d 4d 4f 4e 4b 4c 1a 2a 4g 4h 4j 4i 8a 2e 5P 1a 2a 2b 4a 4b 4c 2c 2d 4d 4e 4f 12a 12b 3a 6a 4g 4h 4i 4j 8a 2e 7P 1a 2a 2b 4a 4c 4b 2c 2d 4d 4f 4e 12b 12a 3a 6a 4g 4h 4j 4i 8a 2e 11P 1a 2a 2b 4a 4c 4b 2c 2d 4d 4f 4e 12b 12a 3a 6a 4g 4h 4j 4i 8a 2e 13P 1a 2a 2b 4a 4b 4c 2c 2d 4d 4e 4f 12a 12b 3a 6a 4g 4h 4i 4j 8a 2e 17P 1a 2a 2b 4a 4b 4c 2c 2d 4d 4e 4f 12a 12b 3a 6a 4g 4h 4i 4j 8a 2e 19P 1a 2a 2b 4a 4c 4b 2c 2d 4d 4f 4e 12b 12a 3a 6a 4g 4h 4j 4i 8a 2e 23P 1a 2a 2b 4a 4c 4b 2c 2d 4d 4f 4e 12b 12a 3a 6a 4g 4h 4j 4i 8a 2e X.1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X.2 1 1 1 1 1 1 -1 -1 -1 -1 -1 1 1 1 1 1 1 1 1 1 1 X.3 4 -4 . . A -A 2 -2 . F -F H -H 1 -1 2 -2 F -F . . X.4 4 -4 . . A -A -2 2 . -F F H -H 1 -1 2 -2 F -F . . X.5 4 -4 . . -A A 2 -2 . -F F -H H 1 -1 2 -2 -F F . . X.6 4 -4 . . -A A -2 2 . F -F -H H 1 -1 2 -2 -F F . . X.7 5 5 5 5 5 5 1 1 1 1 1 -1 -1 -1 -1 1 1 1 1 1 1 X.8 5 5 5 5 5 5 -1 -1 -1 -1 -1 -1 -1 -1 -1 1 1 1 1 1 1 X.9 5 5 5 5 5 5 -3 -3 -3 -3 -3 2 2 2 2 1 1 1 1 1 1 X.10 5 5 5 5 5 5 3 3 3 3 3 2 2 2 2 1 1 1 1 1 1 X.11 6 6 -2 2 -6 -6 . . . . . . . . . 2 2 -2 -2 . -2 X.12 6 6 -2 2 -6 -6 . . . . . . . . . 2 2 -2 -2 . -2 X.13 9 9 9 9 9 9 -3 -3 -3 -3 -3 . . . . 1 1 1 1 1 1 X.14 9 9 9 9 9 9 3 3 3 3 3 . . . . 1 1 1 1 1 1 X.15 10 10 10 10 10 10 -2 -2 -2 -2 -2 1 1 1 1 -2 -2 -2 -2 -2 -2 X.16 10 10 10 10 10 10 2 2 2 2 2 1 1 1 1 -2 -2 -2 -2 -2 -2 X.17 10 10 2 -2 -10 -10 -4 -4 . 4 4 -1 -1 1 1 2 2 -2 -2 . 2 X.18 10 10 2 -2 -10 -10 -4 -4 . 4 4 -1 -1 1 1 2 2 -2 -2 . 2 X.19 10 10 2 -2 -10 -10 4 4 . -4 -4 -1 -1 1 1 2 2 -2 -2 . 2 X.20 10 10 2 -2 -10 -10 4 4 . -4 -4 -1 -1 1 1 2 2 -2 -2 . 2 X.21 15 15 -1 -1 15 15 -3 -3 1 -3 -3 . . . . 3 3 3 3 -1 -1 X.22 15 15 -1 -1 15 15 3 3 -1 3 3 . . . . 3 3 3 3 -1 -1 X.23 15 15 -1 -1 15 15 -3 -3 1 -3 -3 . . . . -1 -1 -1 -1 -1 3 X.24 15 15 -1 -1 15 15 3 3 -1 3 3 . . . . -1 -1 -1 -1 -1 3 X.25 16 16 16 16 16 16 . . . . . -2 -2 -2 -2 . . . . . . X.26 20 20 4 -4 -20 -20 . . . . . -2 -2 2 2 -4 -4 4 4 . -4 X.27 20 -20 . . B -B 2 -2 . F -F -H H -1 1 2 -2 F -F . . X.28 20 -20 . . B -B -2 2 . -F F -H H -1 1 2 -2 F -F . . X.29 20 -20 . . -B B 2 -2 . -F F H -H -1 1 2 -2 -F F . . X.30 20 -20 . . -B B -2 2 . F -F H -H -1 1 2 -2 -F F . . X.31 20 -20 . . B -B -6 6 . G -G F -F 2 -2 2 -2 F -F . . X.32 20 -20 . . B -B 6 -6 . -G G F -F 2 -2 2 -2 F -F . . X.33 20 -20 . . -B B -6 6 . -G G -F F 2 -2 2 -2 -F F . . X.34 20 -20 . . -B B 6 -6 . G -G -F F 2 -2 2 -2 -F F . . X.35 24 24 -8 8 -24 -24 . . . . . . . . . . . . . . . X.36 24 24 -8 8 -24 -24 . . . . . . . . . . . . . . . X.37 30 30 -2 -2 30 30 -6 -6 2 -6 -6 . . . . 2 2 2 2 -2 2 X.38 30 30 -2 -2 30 30 6 6 -2 6 6 . . . . 2 2 2 2 -2 2 X.39 30 30 -10 10 -30 -30 . . . . . . . . . 2 2 -2 -2 . -2 X.40 30 30 -10 10 -30 -30 . . . . . . . . . 2 2 -2 -2 . -2 X.41 36 36 -12 12 -36 -36 . . . . . . . . . -4 -4 4 4 . 4 X.42 36 -36 . . C -C -6 6 . G -G . . . . 2 -2 F -F . . X.43 36 -36 . . C -C 6 -6 . -G G . . . . 2 -2 F -F . . X.44 36 -36 . . -C C -6 6 . -G G . . . . 2 -2 -F F . . X.45 36 -36 . . -C C 6 -6 . G -G . . . . 2 -2 -F F . . X.46 40 40 8 -8 -40 -40 -8 -8 . 8 8 -1 -1 1 1 . . . . . . X.47 40 40 8 -8 -40 -40 8 8 . -8 -8 -1 -1 1 1 . . . . . . X.48 40 40 8 -8 -40 -40 . . . . . 2 2 -2 -2 . . . . . . X.49 40 40 8 -8 -40 -40 . . . . . 2 2 -2 -2 . . . . . . X.50 40 -40 . . D -D -4 4 . A -A H -H 1 -1 -4 4 A -A . . X.51 40 -40 . . D -D 4 -4 . -A A H -H 1 -1 -4 4 A -A . . X.52 40 -40 . . -D D -4 4 . -A A -H H 1 -1 -4 4 -A A . . X.53 40 -40 . . -D D 4 -4 . A -A -H H 1 -1 -4 4 -A A . . X.54 45 45 -3 -3 45 45 -3 -3 1 -3 -3 . . . . -3 -3 -3 -3 1 1 X.55 45 45 -3 -3 45 45 3 3 -1 3 3 . . . . -3 -3 -3 -3 1 1 X.56 45 45 -3 -3 45 45 -3 -3 1 -3 -3 . . . . 1 1 1 1 1 -3 X.57 45 45 -3 -3 45 45 3 3 -1 3 3 . . . . 1 1 1 1 1 -3 X.58 64 -64 . . E -E . . . . . -F F -2 2 . . . . . . X.59 64 -64 . . -E E . . . . . F -F -2 2 . . . . . . 2 7 6 6 6 6 4 3 3 3 3 9 9 9 9 7 6 6 4 6 3 . . . . . . 1 1 1 1 1 1 1 1 . 1 1 . . 5 . . . . . . . . . . . . . . . . . . . 4k 8b 8c 8d 8e 4l 6b 6c 12c 12d 4m 4n 4o 4p 4q 8f 8g 8h 8i 2P 2a 4j 4j 4i 4i 2e 3a 3a 6a 6a 2b 2b 2b 2b 2b 4b 4c 4k 4j 3P 4k 8d 8e 8b 8c 4l 2d 2c 4f 4e 4o 4p 4m 4n 4q 8g 8f 8h 8l 5P 4k 8b 8c 8d 8e 4l 6b 6c 12c 12d 4m 4n 4o 4p 4q 8f 8g 8h 8i 7P 4k 8d 8e 8b 8c 4l 6b 6c 12d 12c 4o 4p 4m 4n 4q 8g 8f 8h 8l 11P 4k 8d 8e 8b 8c 4l 6b 6c 12d 12c 4o 4p 4m 4n 4q 8g 8f 8h 8l 13P 4k 8b 8c 8d 8e 4l 6b 6c 12c 12d 4m 4n 4o 4p 4q 8f 8g 8h 8i 17P 4k 8b 8c 8d 8e 4l 6b 6c 12c 12d 4m 4n 4o 4p 4q 8f 8g 8h 8i 19P 4k 8d 8e 8b 8c 4l 6b 6c 12d 12c 4o 4p 4m 4n 4q 8g 8f 8h 8l 23P 4k 8d 8e 8b 8c 4l 6b 6c 12d 12c 4o 4p 4m 4n 4q 8g 8f 8h 8l X.1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X.2 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 1 1 X.3 . I -I /I -/I . 1 -1 -H H J -J /J -/J . . . . /I X.4 . -I I -/I /I . -1 1 H -H -J J -/J /J . . . . /I X.5 . /I -/I I -I . 1 -1 H -H /J -/J J -J . . . . I X.6 . -/I /I -I I . -1 1 -H H -/J /J -J J . . . . I X.7 1 -1 -1 -1 -1 -1 1 1 1 1 -3 -3 -3 -3 -3 -3 -3 -1 -1 X.8 1 1 1 1 1 1 -1 -1 -1 -1 3 3 3 3 3 3 3 -1 -1 X.9 1 -1 -1 -1 -1 -1 . . . . 1 1 1 1 1 1 1 -1 -1 X.10 1 1 1 1 1 1 . . . . -1 -1 -1 -1 -1 -1 -1 -1 -1 X.11 2 -F -F F F . . . . . -A -A A A . -F F . . X.12 2 F F -F -F . . . . . A A -A -A . F -F . . X.13 1 1 1 1 1 1 . . . . -3 -3 -3 -3 -3 -3 -3 1 1 X.14 1 -1 -1 -1 -1 -1 . . . . 3 3 3 3 3 3 3 1 1 X.15 -2 . . . . . 1 1 1 1 2 2 2 2 2 2 2 . . X.16 -2 . . . . . -1 -1 -1 -1 -2 -2 -2 -2 -2 -2 -2 . . X.17 -2 . . . . . -1 -1 1 1 A A -A -A . -F F . F X.18 -2 . . . . . -1 -1 1 1 -A -A A A . F -F . -F X.19 -2 . . . . . 1 1 -1 -1 A A -A -A . -F F . -F X.20 -2 . . . . . 1 1 -1 -1 -A -A A A . F -F . F X.21 -1 -1 -1 -1 -1 1 . . . . -7 -7 -7 -7 1 1 1 -1 1 X.22 -1 1 1 1 1 -1 . . . . 7 7 7 7 -1 -1 -1 -1 1 X.23 3 1 1 1 1 -1 . . . . 5 5 5 5 -3 1 1 1 -1 X.24 3 -1 -1 -1 -1 1 . . . . -5 -5 -5 -5 3 -1 -1 1 -1 X.25 . . . . . . . . . . . . . . . . . . . X.26 4 . . . . . . . . . . . . . . . . . . X.27 . -I I -/I /I . 1 -1 -H H K -K /K -/K . . . . -/I X.28 . I -I /I -/I . -1 1 H -H -K K -/K /K . . . . -/I X.29 . -/I /I -I I . 1 -1 H -H /K -/K K -K . . . . -I X.30 . /I -/I I -I . -1 1 -H H -/K /K -K K . . . . -I X.31 . -I I -/I /I . . . . . J -J /J -/J . . . . -/I X.32 . I -I /I -/I . . . . . -J J -/J /J . . . . -/I X.33 . -/I /I -I I . . . . . /J -/J J -J . . . . -I X.34 . /I -/I I -I . . . . . -/J /J -J J . . . . -I X.35 . . . . . . . . . . L L -L -L . A -A . . X.36 . . . . . . . . . . -L -L L L . -A A . . X.37 2 . . . . . . . . . -2 -2 -2 -2 -2 2 2 . . X.38 2 . . . . . . . . . 2 2 2 2 2 -2 -2 . . X.39 2 F F -F -F . . . . . -A -A A A . -F F . . X.40 2 -F -F F F . . . . . A A -A -A . F -F . . X.41 -4 . . . . . . . . . . . . . . . . . . X.42 . I -I /I -/I . . . . . K -K /K -/K . . . . /I X.43 . -I I -/I /I . . . . . -K K -/K /K . . . . /I X.44 . /I -/I I -I . . . . . /K -/K K -K . . . . I X.45 . -/I /I -I I . . . . . -/K /K -K K . . . . I X.46 . . . . . . 1 1 -1 -1 . . . . . . . . . X.47 . . . . . . -1 -1 1 1 . . . . . . . . . X.48 . . . . . . . . . . -L -L L L . A -A . . X.49 . . . . . . . . . . L L -L -L . -A A . . X.50 . . . . . . 1 -1 -H H M -M /M -/M . . . . . X.51 . . . . . . -1 1 H -H -M M -/M /M . . . . . X.52 . . . . . . 1 -1 H -H /M -/M M -M . . . . . X.53 . . . . . . -1 1 -H H -/M /M -M M . . . . . X.54 1 1 1 1 1 -1 . . . . -3 -3 -3 -3 5 -3 -3 -1 1 X.55 1 -1 -1 -1 -1 1 . . . . 3 3 3 3 -5 3 3 -1 1 X.56 -3 -1 -1 -1 -1 1 . . . . 9 9 9 9 1 -3 -3 1 -1 X.57 -3 1 1 1 1 -1 . . . . -9 -9 -9 -9 -1 3 3 1 -1 X.58 . . . . . . . . . . . . . . . . . . . X.59 . . . . . . . . . . . . . . . . . . . 2 6 6 6 2 2 2 2 4 5 5 5 5 4 4 4 3 3 4 3 . . . . . . . 1 2 2 2 2 1 1 1 1 1 1 5 . . . 1 1 1 1 . . . . . . . . . . . 8j 8k 8l 10a 5a 20a 20b 12e 6d 3b 12f 12g 6e 12h 12i 24a 24b 12j 2P 4j 4i 4i 5a 5a 10a 10a 6d 3b 3b 6d 6d 3b 6e 6e 12f 12g 6e 3P 8k 8j 8i 10a 5a 20b 20a 4a 2a 1a 4b 4c 2b 4m 4n 8f 8g 4p 5P 8j 8k 8l 2a 1a 4c 4b 12e 6d 3b 12f 12g 6e 12h 12i 24a 24b 12j 7P 8k 8j 8i 10a 5a 20b 20a 12e 6d 3b 12g 12f 6e 12k 12j 24b 24a 12i 11P 8k 8j 8i 10a 5a 20b 20a 12e 6d 3b 12g 12f 6e 12k 12j 24b 24a 12i 13P 8j 8k 8l 10a 5a 20a 20b 12e 6d 3b 12f 12g 6e 12h 12i 24a 24b 12j 17P 8j 8k 8l 10a 5a 20a 20b 12e 6d 3b 12f 12g 6e 12h 12i 24a 24b 12j 19P 8k 8j 8i 10a 5a 20b 20a 12e 6d 3b 12g 12f 6e 12k 12j 24b 24a 12i 23P 8k 8j 8i 10a 5a 20b 20a 12e 6d 3b 12g 12f 6e 12k 12j 24b 24a 12i X.1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X.2 1 1 1 1 1 1 1 1 1 1 1 1 1 -1 -1 -1 -1 -1 X.3 -/I -I I 1 -1 -H H . 2 -2 -F F . -I I . . /I X.4 -/I -I I 1 -1 -H H . 2 -2 -F F . I -I . . -/I X.5 -I -/I /I 1 -1 H -H . 2 -2 F -F . -/I /I . . I X.6 -I -/I /I 1 -1 H -H . 2 -2 F -F . /I -/I . . -I X.7 -1 -1 -1 . . . . 2 2 2 2 2 2 . . . . . X.8 -1 -1 -1 . . . . 2 2 2 2 2 2 . . . . . X.9 -1 -1 -1 . . . . -1 -1 -1 -1 -1 -1 1 1 1 1 1 X.10 -1 -1 -1 . . . . -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 X.11 . . . 1 1 -1 -1 -1 3 3 -3 -3 1 -H -H -H H H X.12 . . . 1 1 -1 -1 -1 3 3 -3 -3 1 H H H -H -H X.13 1 1 1 -1 -1 -1 -1 . . . . . . . . . . . X.14 1 1 1 -1 -1 -1 -1 . . . . . . . . . . . X.15 . . . . . . . 1 1 1 1 1 1 -1 -1 -1 -1 -1 X.16 . . . . . . . 1 1 1 1 1 1 1 1 1 1 1 X.17 F -F -F . . . . 1 1 1 -1 -1 -1 H H -H H -H X.18 -F F F . . . . 1 1 1 -1 -1 -1 -H -H H -H H X.19 -F F F . . . . 1 1 1 -1 -1 -1 H H -H H -H X.20 F -F -F . . . . 1 1 1 -1 -1 -1 -H -H H -H H X.21 1 1 1 . . . . -1 3 3 3 3 -1 -1 -1 1 1 -1 X.22 1 1 1 . . . . -1 3 3 3 3 -1 1 1 -1 -1 1 X.23 -1 -1 -1 . . . . -1 3 3 3 3 -1 -1 -1 1 1 -1 X.24 -1 -1 -1 . . . . -1 3 3 3 3 -1 1 1 -1 -1 1 X.25 . . . 1 1 1 1 -2 -2 -2 -2 -2 -2 . . . . . X.26 . . . . . . . 2 2 2 -2 -2 -2 . . . . . X.27 /I I -I . . . . . 4 -4 A -A . . . . . . X.28 /I I -I . . . . . 4 -4 A -A . . . . . . X.29 I /I -/I . . . . . 4 -4 -A A . . . . . . X.30 I /I -/I . . . . . 4 -4 -A A . . . . . . X.31 /I I -I . . . . . -2 2 F -F . -I I . . /I X.32 /I I -I . . . . . -2 2 F -F . I -I . . -/I X.33 I /I -/I . . . . . -2 2 -F F . -/I /I . . I X.34 I /I -/I . . . . . -2 2 -F F . /I -/I . . -I X.35 . . . -1 -1 1 1 -1 3 3 -3 -3 1 H H H -H -H X.36 . . . -1 -1 1 1 -1 3 3 -3 -3 1 -H -H -H H H X.37 . . . . . . . 1 -3 -3 -3 -3 1 1 1 -1 -1 1 X.38 . . . . . . . 1 -3 -3 -3 -3 1 -1 -1 1 1 -1 X.39 . . . . . . . 1 -3 -3 3 3 -1 -H -H -H H H X.40 . . . . . . . 1 -3 -3 3 3 -1 H H H -H -H X.41 . . . 1 1 -1 -1 . . . . . . . . . . . X.42 -/I -I I -1 1 H -H . . . . . . . . . . . X.43 -/I -I I -1 1 H -H . . . . . . . . . . . X.44 -I -/I /I -1 1 -H H . . . . . . . . . . . X.45 -I -/I /I -1 1 -H H . . . . . . . . . . . X.46 . . . . . . . -2 -2 -2 2 2 2 . . . . . X.47 . . . . . . . -2 -2 -2 2 2 2 . . . . . X.48 . . . . . . . 1 1 1 -1 -1 -1 -H -H H -H H X.49 . . . . . . . 1 1 1 -1 -1 -1 H H -H H -H X.50 . . . . . . . . 2 -2 -F F . I -I . . -/I X.51 . . . . . . . . 2 -2 -F F . -I I . . /I X.52 . . . . . . . . 2 -2 F -F . /I -/I . . -I X.53 . . . . . . . . 2 -2 F -F . -/I /I . . I X.54 1 1 1 . . . . . . . . . . . . . . . X.55 1 1 1 . . . . . . . . . . . . . . . X.56 -1 -1 -1 . . . . . . . . . . . . . . . X.57 -1 -1 -1 . . . . . . . . . . . . . . . X.58 . . . 1 -1 -H H . -4 4 -A A . . . . . . X.59 . . . 1 -1 H -H . -4 4 A -A . . . . . . 2 4 3 1 5 . 12k 2P 6e 3P 4o 5P 12k 7P 12h 11P 12h 13P 12k 17P 12k 19P 12h 23P 12h X.1 1 X.2 -1 X.3 -/I X.4 /I X.5 -I X.6 I X.7 . X.8 . X.9 1 X.10 -1 X.11 H X.12 -H X.13 . X.14 . X.15 -1 X.16 1 X.17 -H X.18 H X.19 -H X.20 H X.21 -1 X.22 1 X.23 -1 X.24 1 X.25 . X.26 . X.27 . X.28 . X.29 . X.30 . X.31 -/I X.32 /I X.33 -I X.34 I X.35 -H X.36 H X.37 1 X.38 -1 X.39 H X.40 -H X.41 . X.42 . X.43 . X.44 . X.45 . X.46 . X.47 . X.48 H X.49 -H X.50 /I X.51 -/I X.52 I X.53 -I X.54 . X.55 . X.56 . X.57 . X.58 . X.59 . A = -4*E(4) = -4*ER(-1) = -4i B = -20*E(4) = -20*ER(-1) = -20i C = -36*E(4) = -36*ER(-1) = -36i D = -40*E(4) = -40*ER(-1) = -40i E = -64*E(4) = -64*ER(-1) = -64i F = 2*E(4) = 2*ER(-1) = 2i G = -6*E(4) = -6*ER(-1) = -6i H = E(4) = ER(-1) = i I = 1+E(4) = 1+ER(-1) = 1+i J = 2-2*E(4) = 2-2*ER(-1) = 2-2i K = -6+6*E(4) = -6+6*ER(-1) = -6+6i L = 8*E(4) = 8*ER(-1) = 8i M = 4-4*E(4) = 4-4*ER(-1) = 4-4i gap> quit;