2.cos(2*n*pi/97)?

I.

A1111=2*(cos(2*pi/97)+cos(70*pi/97)+cos(122*pi/97));

A1112=2*(cos(150*pi/97)+cos(12*pi/97)+cos(32*pi/97));

A1121=2*(cos(100*pi/97)+cos(8*pi/97)+cos(86*pi/97));

A1122=2*(cos(128*pi/97)+cos(18*pi/97)+cos(48*pi/97));

A1211=2*(cos(4*pi/97)+cos(140*pi/97)+cos(50*pi/97));

A1212=2*(cos(106*pi/97)+cos(24*pi/97)+cos(64*pi/97));

A1221=2*(cos(6*pi/97)+cos(16*pi/97)+cos(172*pi/97));

A1222=2*(cos(62*pi/97)+cos(36*pi/97)+cos(96*pi/97));

A2111=2*(cos(10*pi/97)+cos(156*pi/97)+cos(28*pi/97));

A2112=2*(cos(26*pi/97)+cos(134*pi/97)+cos(34*pi/97));

A2121=2*(cos(112*pi/97)+cos(40*pi/97)+cos(42*pi/97));

A2122=2*(cos(58*pi/97)+cos(90*pi/97)+cos(46*pi/97));

A2211=2*(cos(20*pi/97)+cos(118*pi/97)+cos(56*pi/97));

A2212=2*(cos(52*pi/97)+cos(74*pi/97)+cos(68*pi/97));

A2221=2*(cos(78*pi/97)+cos(14*pi/97)+cos(102*pi/97));

A2222=2*(cos(30*pi/97)+cos(80*pi/97)+cos(84*pi/97));

A1111+A1112+A1121+A1122+A1211+A1212+A1221+A1222+A2111+A2112+A2121+A2122+A2211+A2212+A2221+A2222=-1;

A1111+A1112+A1121+A1122+A1211+A1212+A1221+A1222-(A2111+A2112+A2121+A2122+A2211+A2212+A2221+A2222)

=sqrt(97);

(A1111+A1112+A1121+A1122-(A1211+A1212+A1221+A1222))^2+(A2111+A2112+A2121+A2122-(A2211+A2212+A2221+A2222))^2=97;

(A1111+A1112+A1121+A1122-(A1211+A1212+A1221+A1222))^2-(A2111+A2112+A2121+A2122-(A2211+A2212+A2221+A2222))^2=-9*sqrt(97);

(A1111+A1112-A1121-A1122)^2+(A1211+A1212-A1221-A1222)^2+(A2111+A2112-A2121-A2122)^2+(A2211+A2212-A2221-A2222)^2=97;

(A1111+A1112-A1121-A1122)^2+(A1211+A1212-A1221-A1222)^2-(A2111+A2112-A2121-A2122)^2-(A2211+A2212-A2221-A2222)^2=-5*sqrt(97);

((A1111+A1112-A1121-A1122)^2-(A1211+A1212-A1221-A1222)^2)^2+((A2111+A2112-A2121-A2122)^2-(A2211+A2212-A2221-A2222)^2)^2=5141;

((A1111+A1112-A1121-A1122)^2-(A1211+A1212-A1221-A1222)^2)^2-((A2111+A2112-A2121-A2122)^2-(A2211+A2212-A2221-A2222)^2)^2=-517*sqrt(97);

(A1111-A1112)^2+(A1121-A1122)^2+(A1211-A1212)^2+(A1221-A1222)^2+(A2111-A2112)^2+(A2121-A2122)^2+(A2211-A2212)^2+(A2221-A2222)^2=97;

(A1111-A1112)^2+(A1121-A1122)^2+(A1211-A1212)^2+(A1221-A1222)^2-(A2111-A2112)^2-(A2121-A2122)^2-(A2211-A2212)^2-(A2221-A2222)^2=7*sqrt(97);

((A1111-A1112)^2+(A1121-A1122)^2-(A1211-A1212)^2-(A1221-A1222)^2)^2+((A2111-A2112)^2+(A2121-A2122)^2-(A2211-A2212)^2-(A2221-A2222)^2)^2=1649;

((A1111-A1112)^2+(A1121-A1122)^2-(A1211-A1212)^2-(A1221-A1222)^2)^2-((A2111-A2112)^2+(A2121-A2122)^2-(A2211-A2212)^2-(A2221-A2222)^2)^2=167*sqrt(97);

((A1111-A1112)^2-(A1121-A1122)^2)^2+((A1211-A1212)^2-(A1221-A1222)^2)^2+((A2111-A2112)^2-(A2121-A2122)^2)^2+((A2211-A2212)^2-(A2221-A2222)^2)^2=2037;

((A1111-A1112)^2-(A1121-A1122)^2)^2+((A1211-A1212)^2-(A1221-A1222)^2)^2-((A2111-A2112)^2-(A2121-A2122)^2)^2-((A2211-A2212)^2-(A2221-A2222)^2)^2=199*sqrt(97);

(((A1111-A1112)^2-(A1121-A1122)^2)^2-((A1211-A1212)^2-(A1221-A1222)^2)^2)^2+(((A2111-A2112)^2-(A2121-A2122)^2)^2-((A2211-A2212)^2-(A2221-A2222)^2)^2)^2=3488605;

(((A1111-A1112)^2-(A1121-A1122)^2)^2-((A1211-A1212)^2-(A1221-A1222)^2)^2)^2-(((A2111-A2112)^2-(A2121-A2122)^2)^2-((A2211-A2212)^2-(A2221-A2222)^2)^2)^2=354099*sqrt(97).

?

A1111=(-1+sqrt(97)-sqrt(194-18*sqrt(97))+2*sqrt(97-5*sqrt(97)+sqrt(10282-1034*sqrt(97)))-2*sqrt(194+14*sqrt(97)-2*sqrt(3298+334*sqrt(97))+4*sqrt(2037+199*sqrt(97)-sqrt(6977210+708198*sqrt(97)))))/16;

A1112=(-1+sqrt(97)-sqrt(194-18*sqrt(97))+2*sqrt(97-5*sqrt(97)+sqrt(10282-1034*sqrt(97)))+2*sqrt(194+14*sqrt(97)-2*sqrt(3298+334*sqrt(97))+4*sqrt(2037+199*sqrt(97)-sqrt(6977210+708198*sqrt(97)))))/16;

A1121=(-1+sqrt(97)-sqrt(194-18*sqrt(97))-2*sqrt(97-5*sqrt(97)+sqrt(10282-1034*sqrt(97)))-2*sqrt(194+14*sqrt(97)-2*sqrt(3298+334*sqrt(97))-4*sqrt(2037+199*sqrt(97)-sqrt(6977210+708198*sqrt(97)))))/16;

A1122=(-1+sqrt(97)-sqrt(194-18*sqrt(97))-2*sqrt(97-5*sqrt(97)+sqrt(10282-1034*sqrt(97)))+2*sqrt(194+14*sqrt(97)-2*sqrt(3298+334*sqrt(97))-4*sqrt(2037+199*sqrt(97)-sqrt(6977210+708198*sqrt(97)))))/16;

A1211=(-1+sqrt(97)+sqrt(194-18*sqrt(97))-2*sqrt(97-5*sqrt(97)-sqrt(10282-1034*sqrt(97)))+2*sqrt(194+14*sqrt(97)+2*sqrt(3298+334*sqrt(97))-4*sqrt(2037+199*sqrt(97)+sqrt(6977210+708198*sqrt(97)))))/16;

A1212=(-1+sqrt(97)+sqrt(194-18*sqrt(97))-2*sqrt(97-5*sqrt(97)-sqrt(10282-1034*sqrt(97)))-2*sqrt(194+14*sqrt(97)+2*sqrt(3298+334*sqrt(97))-4*sqrt(2037+199*sqrt(97)+sqrt(6977210+708198*sqrt(97)))))/16;

A1221=(-1+sqrt(97)+sqrt(194-18*sqrt(97))+2*sqrt(97-5*sqrt(97)-sqrt(10282-1034*sqrt(97)))+2*sqrt(194+14*sqrt(97)+2*sqrt(3298+334*sqrt(97))+4*sqrt(2037+199*sqrt(97)+sqrt(6977210+708198*sqrt(97)))))/16;

A1222=(-1+sqrt(97)+sqrt(194-18*sqrt(97))+2*sqrt(97-5*sqrt(97)-sqrt(10282-1034*sqrt(97)))-2*sqrt(194+14*sqrt(97)+2*sqrt(3298+334*sqrt(97))+4*sqrt(2037+199*sqrt(97)+sqrt(6977210+708198*sqrt(97)))))/16;

A2111=(-1-sqrt(97)+sqrt(194+18*sqrt(97))+2*sqrt(97+5*sqrt(97)+sqrt(10282+1034*sqrt(97)))+2*sqrt(194-14*sqrt(97)+2*sqrt(3298-334*sqrt(97))+4*sqrt(2037-199*sqrt(97)-sqrt(6977210-708198*sqrt(97)))))/16;

A2112=(-1-sqrt(97)+sqrt(194+18*sqrt(97))+2*sqrt(97+5*sqrt(97)+sqrt(10282+1034*sqrt(97)))-2*sqrt(194-14*sqrt(97)+2*sqrt(3298-334*sqrt(97))+4*sqrt(2037-199*sqrt(97)-sqrt(6977210-708198*sqrt(97)))))/16;

A2121=(-1-sqrt(97)+sqrt(194+18*sqrt(97))-2*sqrt(97+5*sqrt(97)+sqrt(10282+1034*sqrt(97)))+2*sqrt(194-14*sqrt(97)+2*sqrt(3298-334*sqrt(97))-4*sqrt(2037-199*sqrt(97)-sqrt(6977210-708198*sqrt(97)))))/16;

A2122=(-1-sqrt(97)+sqrt(194+18*sqrt(97))-2*sqrt(97+5*sqrt(97)+sqrt(10282+1034*sqrt(97)))-2*sqrt(194-14*sqrt(97)+2*sqrt(3298-334*sqrt(97))-4*sqrt(2037-199*sqrt(97)-sqrt(6977210-708198*sqrt(97)))))/16;

A2211=(-1-sqrt(97)-sqrt(194+18*sqrt(97))+2*sqrt(97+5*sqrt(97)-sqrt(10282+1034*sqrt(97)))+2*sqrt(194-14*sqrt(97)-2*sqrt(3298-334*sqrt(97))+4*sqrt(2037-199*sqrt(97)+sqrt(6977210-708198*sqrt(97)))))/16;

A2212=(-1-sqrt(97)-sqrt(194+18*sqrt(97))+2*sqrt(97+5*sqrt(97)-sqrt(10282+1034*sqrt(97)))-2*sqrt(194-14*sqrt(97)-2*sqrt(3298-334*sqrt(97))+4*sqrt(2037-199*sqrt(97)+sqrt(6977210-708198*sqrt(97)))))/16;

A2221=(-1-sqrt(97)-sqrt(194+18*sqrt(97))-2*sqrt(97+5*sqrt(97)-sqrt(10282+1034*sqrt(97)))+2*sqrt(194-14*sqrt(97)-2*sqrt(3298-334*sqrt(97))-4*sqrt(2037-199*sqrt(97)+sqrt(6977210-708198*sqrt(97)))))/16;

A2222=(-1-sqrt(97)-sqrt(194+18*sqrt(97))-2*sqrt(97+5*sqrt(97)-sqrt(10282+1034*sqrt(97)))-2*sqrt(194-14*sqrt(97)-2*sqrt(3298-334*sqrt(97))-4*sqrt(2037-199*sqrt(97)+sqrt(6977210-708198*sqrt(97)))))/16;

?

II.

B1111=4*(cos(2*pi/97)*cos(70*pi/97)+cos(70*pi/97)*cos(122*pi/97)+cos(122*pi/97)*cos(2*pi/97));

B1112=4*(cos(150*pi/97)*cos(12*pi/97)+cos(12*pi/97)*cos(32*pi/97)+cos(32*pi/97)*cos(150*pi/97));

B1121=4*(cos(100*pi/97)*cos(8*pi/97)+cos(8*pi/97)*cos(86*pi/97)+cos(86*pi/97)*cos(100*pi/97));

B1122=4*(cos(128*pi/97)*cos(18*pi/97)+cos(18*pi/97)*cos(48*pi/97)+cos(48*pi/97)*cos(128*pi/97));

B1211=4*(cos(4*pi/97)*cos(140*pi/97)+cos(140*pi/97)*cos(50*pi/97)+cos(50*pi/97)*cos(4*pi/97));

B1212=4*(cos(106*pi/97)*cos(24*pi/97)+cos(24*pi/97)*cos(64*pi/97)+cos(64*pi/97)*cos(106*pi/97));

B1221=4*(cos(6*pi/97)*cos(16*pi/97)+cos(16*pi/97)*cos(172*pi/97)+cos(172*pi/97)*cos(6*pi/97));

B1222=4*(cos(62*pi/97)*cos(36*pi/97)+cos(36*pi/97)*cos(96*pi/97)+cos(96*pi/97)*cos(62*pi/97));

B2111=4*(cos(10*pi/97)*cos(156*pi/97)+cos(156*pi/97)*cos(28*pi/97)+cos(28*pi/97)*cos(10*pi/97));

B2112=4*(cos(26*pi/97)*cos(134*pi/97)+cos(134*pi/97)*cos(34*pi/97)+cos(34*pi/97)*cos(26*pi/97));

B2121=4*(cos(112*pi/97)*cos(40*pi/97)+cos(40*pi/97)*cos(42*pi/97)+cos(42*pi/97)*cos(112*pi/97));

B2122=4*(cos(58*pi/97)*cos(90*pi/97)+cos(90*pi/97)*cos(46*pi/97)+cos(46*pi/97)*cos(58*pi/97));

B2211=4*(cos(20*pi/97)*cos(118*pi/97)+cos(118*pi/97)*cos(56*pi/97)+cos(56*pi/97)*cos(20*pi/97));

B2212=4*(cos(52*pi/97)*cos(74*pi/97)+cos(74*pi/97)*cos(68*pi/97)+cos(68*pi/97)*cos(52*pi/97));

B2221=4*(cos(78*pi/97)*cos(14*pi/97)+cos(14*pi/97)*cos(102*pi/97)+cos(102*pi/97)*cos(78*pi/97));

B2222=4*(cos(30*pi/97)*cos(80*pi/97)+cos(80*pi/97)*cos(84*pi/97)+cos(84*pi/97)*cos(30*pi/97));

B1111+B1112 + B1121+B1122 + B1211+B1212 + B1221+B1222 +B2111+B2112+B2121+B2122+B2211+B2212+B2221+B2222=-2

B1111+B1112 + B1121+B1122 + B1211+B1212 + B1221+B1222-(B2111+B2112+B2121+B2122+B2211+B2212+B2221+B2222)=0

(B1111+B1112 + B1121+B1122 -?B1211-B1212-?B1221-B1222)^2+(B2111+B2112+B2121+B2122-B2211-B2212-B2221-B2222)^2

=194;

(B1111+B1112 + B1121+B1122 -?B1211-B1212-?B1221-B1222)^2-(B2111+B2112+B2121+B2122-B2211-B2212-B2221-B2222)^2

=8*sqrt(97);

(B1111+B1112-B1121-B1122)^2+(B1211+B1212-B1221-B1222)^2+(B2111+B2112-B2121-B2122)^2+(B2211+B2212-B2221-B2222)^2=194;

(B1111+B1112-B1121-B1122)^2+(B1211+B1212-B1221-B1222)^2-(B2111+B2112-B2121-B2122)^2-(B2211+B2212-B2221-B2222)^2=12*sqrt(97);

((B1111+B1112-B1121-B1122)^2-(B1211+B1212-B1221-B1222)^2)^2+((B2111+B2112-B2121-B2122)^2-(B2211+B2212-B2221-B2222)^2)^2=12610;

((B1111+B1112-B1121-B1122)^2-(B1211+B1212-B1221-B1222)^2)^2-((B2111+B2112-B2121-B2122)^2-(B2211+B2212-B2221-B2222)^2)^2=1272*sqrt(97);

(B1111-B1112)^2+(B1121-B1122)^2+(B1211-B1212)^2+(B1221-B1222)^2+(B2111-B2112)^2+(B2121-B2122)^2+(B2211-B2212)^2+(B2221-B2222)^2=194;

(B1111-B1112)^2+(B1121-B1122)^2+(B1211-B1212)^2+(B1221-B1222)^2-(B2111-B2112)^2-(B2121-B2122)^2-(B2211-B2212)^2-(B2221-B2222)^2=8*sqrt(97);

((B1111-B1112)^2+(B1121-B1122)^2-(B1211-B1212)^2-(B1221-B1222)^2)^2+((B2111-B2112)^2+(B2121-B2122)^2-(B2211-B2212)^2-(B2221-B2222)^2)^2=2522;

((B1111-B1112)^2+(B1121-B1122)^2-(B1211-B1212)^2-(B1221-B1222)^2)^2-((B2111-B2112)^2+(B2121-B2122)^2-(B2211-B2212)^2-(B2221-B2222)^2)^2=256*sqrt(97);

((B1111-B1112)^2-(B1121-B1122)^2)^2+((B1211-B1212)^2-(B1221-B1222)^2)^2+((B2111-B2112)^2-(B2121-B2122)^2)^2+((B2211-B2212)^2-(B2221-B2222)^2)^2=9894;

((B1111-B1112)^2-(B1121-B1122)^2)^2+((B1211-B1212)^2-(B1221-B1222)^2)^2-((B2111-B2112)^2-(B2121-B2122)^2)^2-((B2211-B2212)^2-(B2221-B2222)^2)^2=872*sqrt(97);

(((B1111-B1112)^2-(B1121-B1122)^2)^2-((B1211-B1212)^2-(B1221-B1222)^2)^2)^2+(((B2111-B2112)^2-(B2121-B2122)^2)^2-((B2211-B2212)^2-(B2221-B2222)^2)^2)^2=45452842;

(((B1111-B1112)^2-(B1121-B1122)^2)^2-((B1211-B1212)^2-(B1221-B1222)^2)^2)^2-(((B2111-B2112)^2-(B2121-B2122)^2)^2-((B2211-B2212)^2-(B2221-B2222)^2)^2)^2=4614864*sqrt(97).

B1111+B1112+B1121+B1122=(-1-sqrt(97+4*sqrt(97)))/2;

B1111+B1112=(-1-sqrt(97+4*sqrt(97))+sqrt(194+12*sqrt(97)-2*sqrt(6305+636*sqrt(97))))/4;

?

B1111=(-1-sqrt(97+4*sqrt(97))+sqrt(194+12*sqrt(97)-2*sqrt(6305+636*sqrt(97)))-2*sqrt(97+4*sqrt(97)-sqrt(1261+128*sqrt(97))+sqrt(9894+872*sqrt(97)-2*sqrt(22726421+2307432*sqrt(97)))))/8;

B1112=(-1-sqrt(97+4*sqrt(97))+sqrt(194+12*sqrt(97)-2*sqrt(6305+636*sqrt(97)))+2*sqrt(97+4*sqrt(97)-sqrt(1261+128*sqrt(97))+sqrt(9894+872*sqrt(97)-2*sqrt(22726421+2307432*sqrt(97)))))/8;

B1121=(-1-sqrt(97+4*sqrt(97))-sqrt(194+12*sqrt(97)-2*sqrt(6305+636*sqrt(97)))-2*sqrt(97+4*sqrt(97)-sqrt(1261+128*sqrt(97))-sqrt(9894+872*sqrt(97)-2*sqrt(22726421+2307432*sqrt(97)))))/8;

B1122=(-1-sqrt(97+4*sqrt(97))-sqrt(194+12*sqrt(97)-2*sqrt(6305+636*sqrt(97)))+2*sqrt(97+4*sqrt(97)-sqrt(1261+128*sqrt(97))-sqrt(9894+872*sqrt(97)-2*sqrt(22726421+2307432*sqrt(97)))))/8;

B1211=(-1+sqrt(97+4*sqrt(97))-sqrt(194+12*sqrt(97)+2*sqrt(6305+636*sqrt(97)))+2*sqrt(97+4*sqrt(97)+sqrt(1261+128*sqrt(97))-sqrt(9894+872*sqrt(97)+2*sqrt(22726421+2307432*sqrt(97)))))/8;

B1212=(-1+sqrt(97+4*sqrt(97))-sqrt(194+12*sqrt(97)+2*sqrt(6305+636*sqrt(97)))-2*sqrt(97+4*sqrt(97)+sqrt(1261+128*sqrt(97))-sqrt(9894+872*sqrt(97)+2*sqrt(22726421+2307432*sqrt(97)))))/8;

B1221=(-1+sqrt(97+4*sqrt(97))+sqrt(194+12*sqrt(97)+2*sqrt(6305+636*sqrt(97)))+2*sqrt(97+4*sqrt(97)+sqrt(1261+128*sqrt(97))+sqrt(9894+872*sqrt(97)+2*sqrt(22726421+2307432*sqrt(97)))))/8;

B1222=(-1+sqrt(97+4*sqrt(97))+sqrt(194+12*sqrt(97)+2*sqrt(6305+636*sqrt(97)))-2*sqrt(97+4*sqrt(97)+sqrt(1261+128*sqrt(97))+sqrt(9894+872*sqrt(97)+2*sqrt(22726421+2307432*sqrt(97)))))/8;

B2111=(-1+sqrt(97-4*sqrt(97))+sqrt(194-12*sqrt(97)+2*sqrt(6305-636*sqrt(97)))+2*sqrt(97-4*sqrt(97)-sqrt(1261-128*sqrt(97))+sqrt(9894-872*sqrt(97)+2*sqrt(22726421-2307432*sqrt(97)))))/8;

B2112=(-1+sqrt(97-4*sqrt(97))+sqrt(194-12*sqrt(97)+2*sqrt(6305-636*sqrt(97)))-2*sqrt(97-4*sqrt(97)-sqrt(1261-128*sqrt(97))+sqrt(9894-872*sqrt(97)+2*sqrt(22726421-2307432*sqrt(97)))))/8;

B2121=(-1+sqrt(97-4*sqrt(97))-sqrt(194-12*sqrt(97)+2*sqrt(6305-636*sqrt(97)))-2*sqrt(97-4*sqrt(97)-sqrt(1261-128*sqrt(97))-sqrt(9894-872*sqrt(97)+2*sqrt(22726421-2307432*sqrt(97)))))/8;

B2122=(-1+sqrt(97-4*sqrt(97))-sqrt(194-12*sqrt(97)+2*sqrt(6305-636*sqrt(97)))+2*sqrt(97-4*sqrt(97)-sqrt(1261-128*sqrt(97))-sqrt(9894-872*sqrt(97)+2*sqrt(22726421-2307432*sqrt(97)))))/8;

B2211=(-1-sqrt(97-4*sqrt(97))+sqrt(194-12*sqrt(97)-2*sqrt(6305-636*sqrt(97)))-2*sqrt(97-4*sqrt(97)+sqrt(1261-128*sqrt(97))+sqrt(9894-872*sqrt(97)-2*sqrt(22726421-2307432*sqrt(97)))))/8;

B2212=(-1-sqrt(97-4*sqrt(97))+sqrt(194-12*sqrt(97)-2*sqrt(6305-636*sqrt(97)))+2*sqrt(97-4*sqrt(97)+sqrt(1261-128*sqrt(97))+sqrt(9894-872*sqrt(97)-2*sqrt(22726421-2307432*sqrt(97)))))/8;

B2221=(-1-sqrt(97-4*sqrt(97))-sqrt(194-12*sqrt(97)-2*sqrt(6305-636*sqrt(97)))-2*sqrt(97-4*sqrt(97)+sqrt(1261-128*sqrt(97))-sqrt(9894-872*sqrt(97)-2*sqrt(22726421-2307432*sqrt(97)))))/8;

B2222=(-1-sqrt(97-4*sqrt(97))-sqrt(194-12*sqrt(97)-2*sqrt(6305-636*sqrt(97)))+2*sqrt(97-4*sqrt(97)+sqrt(1261-128*sqrt(97))-sqrt(9894-872*sqrt(97)-2*sqrt(22726421-2307432*sqrt(97)))))/8;

?

III.

C1111=8*(cos(2*pi/97)*cos(70*pi/97)*cos(122*pi/97));

C1112=8*(cos(150*pi/97)*cos(12*pi/97)*cos(32*pi/97));

C1121=8*(cos(100*pi/97)*cos(8*pi/97)*cos(86*pi/97));

C1122=8*(cos(128*pi/97)*cos(18*pi/97)*cos(48*pi/97));

C1211=8*(cos(4*pi/97)*cos(140*pi/97)*cos(50*pi/97));

C1212=8*(cos(106*pi/97)*cos(24*pi/97)*cos(64*pi/97));

C1221=8*(cos(6*pi/97)*cos(16*pi/97)*cos(172*pi/97));

C1222=8*(cos(62*pi/97)*cos(36*pi/97)*cos(96*pi/97));

C2111=8*(cos(10*pi/97)*cos(156*pi/97)*cos(28*pi/97));

C2112=8*(cos(26*pi/97)*cos(134*pi/97)*cos(34*pi/97));

C2121=8*(cos(112*pi/97)*cos(40*pi/97)*cos(42*pi/97));

C2122=8*(cos(58*pi/97)*cos(90*pi/97)*cos(46*pi/97));

C2211=8*(cos(20*pi/97)*cos(118*pi/97)*cos(56*pi/97));

C2212=8*(cos(52*pi/97)*cos(74*pi/97)*cos(68*pi/97));

C2221=8*(cos(78*pi/97)*cos(14*pi/97)*cos(102*pi/97));

C2222=8*(cos(30*pi/97)*cos(80*pi/97)*cos(84*pi/97));

?

C1111=(31+sqrt(97)+sqrt(194-18*sqrt(97))-2*sqrt(97-5*sqrt(97)-sqrt(10282-1034*sqrt(97)))+2*sqrt(194+14*sqrt(97)+2*sqrt(3298+334*sqrt(97))-4*sqrt(2037+199*sqrt(97)+sqrt(6977210+708198*sqrt(97)))))/16;

C1112=(31+sqrt(97)+sqrt(194-18*sqrt(97))-2*sqrt(97-5*sqrt(97)-sqrt(10282-1034*sqrt(97)))-2*sqrt(194+14*sqrt(97)+2*sqrt(3298+334*sqrt(97))-4*sqrt(2037+199*sqrt(97)+sqrt(6977210+708198*sqrt(97)))))/16;

C1121=(31+sqrt(97)+sqrt(194-18*sqrt(97))+2*sqrt(97-5*sqrt(97)-sqrt(10282-1034*sqrt(97)))+2*sqrt(194+14*sqrt(97)+2*sqrt(3298+334*sqrt(97))+4*sqrt(2037+199*sqrt(97)+sqrt(6977210+708198*sqrt(97)))))/16;

C1122=(31+sqrt(97)+sqrt(194-18*sqrt(97))+2*sqrt(97-5*sqrt(97)-sqrt(10282-1034*sqrt(97)))-2*sqrt(194+14*sqrt(97)+2*sqrt(3298+334*sqrt(97))+4*sqrt(2037+199*sqrt(97)+sqrt(6977210+708198*sqrt(97)))))/16;

C1211=(31+sqrt(97)-sqrt(194-18*sqrt(97))-2*sqrt(97-5*sqrt(97)+sqrt(10282-1034*sqrt(97)))-2*sqrt(194+14*sqrt(97)-2*sqrt(3298+334*sqrt(97))-4*sqrt(2037+199*sqrt(97)-sqrt(6977210+708198*sqrt(97)))))/16;

C1212=(31+sqrt(97)-sqrt(194-18*sqrt(97))-2*sqrt(97-5*sqrt(97)+sqrt(10282-1034*sqrt(97)))+2*sqrt(194+14*sqrt(97)-2*sqrt(3298+334*sqrt(97))-4*sqrt(2037+199*sqrt(97)-sqrt(6977210+708198*sqrt(97)))))/16;

C1221=(31+sqrt(97)-sqrt(194-18*sqrt(97))+2*sqrt(97-5*sqrt(97)+sqrt(10282-1034*sqrt(97)))+2*sqrt(194+14*sqrt(97)-2*sqrt(3298+334*sqrt(97))+4*sqrt(2037+199*sqrt(97)-sqrt(6977210+708198*sqrt(97)))))/16;

C1222=(31+sqrt(97)-sqrt(194-18*sqrt(97))+2*sqrt(97-5*sqrt(97)+sqrt(10282-1034*sqrt(97)))-2*sqrt(194+14*sqrt(97)-2*sqrt(3298+334*sqrt(97))+4*sqrt(2037+199*sqrt(97)-sqrt(6977210+708198*sqrt(97)))))/16;

C2111=(31-sqrt(97)-sqrt(194+18*sqrt(97))+2*sqrt(97+5*sqrt(97)-sqrt(10282+1034*sqrt(97)))+2*sqrt(194-14*sqrt(97)-2*sqrt(3298-334*sqrt(97))+4*sqrt(2037-199*sqrt(97)+sqrt(6977210-708198*sqrt(97)))))/16;

C2112=(31-sqrt(97)-sqrt(194+18*sqrt(97))+2*sqrt(97+5*sqrt(97)-sqrt(10282+1034*sqrt(97)))-2*sqrt(194-14*sqrt(97)-2*sqrt(3298-334*sqrt(97))+4*sqrt(2037-199*sqrt(97)+sqrt(6977210-708198*sqrt(97)))))/16;

C2121=(31-sqrt(97)-sqrt(194+18*sqrt(97))-2*sqrt(97+5*sqrt(97)-sqrt(10282+1034*sqrt(97)))-2*sqrt(194-14*sqrt(97)-2*sqrt(3298-334*sqrt(97))-4*sqrt(2037-199*sqrt(97)+sqrt(6977210-708198*sqrt(97)))))/16;

C2122=(31-sqrt(97)-sqrt(194+18*sqrt(97))-2*sqrt(97+5*sqrt(97)-sqrt(10282+1034*sqrt(97)))+2*sqrt(194-14*sqrt(97)-2*sqrt(3298-334*sqrt(97))-4*sqrt(2037-199*sqrt(97)+sqrt(6977210-708198*sqrt(97)))))/16;

C2211=(31-sqrt(97)+sqrt(194+18*sqrt(97))-2*sqrt(97+5*sqrt(97)+sqrt(10282+1034*sqrt(97)))+2*sqrt(194-14*sqrt(97)+2*sqrt(3298-334*sqrt(97))-4*sqrt(2037-199*sqrt(97)-sqrt(6977210-708198*sqrt(97)))))/16;

C2212=(31-sqrt(97)+sqrt(194+18*sqrt(97))-2*sqrt(97+5*sqrt(97)+sqrt(10282+1034*sqrt(97)))-2*sqrt(194-14*sqrt(97)+2*sqrt(3298-334*sqrt(97))-4*sqrt(2037-199*sqrt(97)-sqrt(6977210-708198*sqrt(97)))))/16;

C2221=(31-sqrt(97)+sqrt(194+18*sqrt(97))+2*sqrt(97+5*sqrt(97)+sqrt(10282+1034*sqrt(97)))+2*sqrt(194-14*sqrt(97)+2*sqrt(3298-334*sqrt(97))+4*sqrt(2037-199*sqrt(97)-sqrt(6977210-708198*sqrt(97)))))/16;

C2222=(31-sqrt(97)+sqrt(194+18*sqrt(97))+2*sqrt(97+5*sqrt(97)+sqrt(10282+1034*sqrt(97)))-2*sqrt(194-14*sqrt(97)+2*sqrt(3298-334*sqrt(97))+4*sqrt(2037-199*sqrt(97)-sqrt(6977210-708198*sqrt(97)))))/16;

?

IV.

P1111=2*A1111^3-9*A1111*B1111+27*C1111;

P1112=2*A1112^3-9*A1112*B1112+27*C1112;

P1121=2*A1121^3-9*A1121*B1121+27*C1121;

P1122=2*A1122^3-9*A1122*B1122+27*C1122;

P1211=2*A1211^3-9*A1211*B1211+27*C1211;

P1212=2*A1212^3-9*A1212*B1212+27*C1212;

P1221=2*A1221^3-9*A1221*B1221+27*C1221;

P1222=2*A1222^3-9*A1222*B1222+27*C1222;

P2111=2*A2111^3-9*A2111*B2111+27*C2111;

P2112=2*A2112^3-9*A2112*B2112+27*C2112;

P2121=2*A2121^3-9*A2121*B2121+27*C2121;

P2122=2*A2122^3-9*A2122*B2122+27*C2122;

P2211=2*A2211^3-9*A2211*B2211+27*C2211;

P2212=2*A2212^3-9*A2212*B2212+27*C2212;

P2221=2*A2221^3-9*A2221*B2221+27*C2221;

P2222=2*A2222^3-9*A2222*B2222+27*C2222;

P1111+P1112+P1121+P1122+P1211+P1212+P1221+P1222+P2111+P2112+P2121+P2122+P2211+P2212+P2221+P2222=388;

P1111+P1112+P1121+P1122+P1211+P1212+P1221+P1222-(P2111+P2112+P2121+P2122+P2211+P2212+P2221+P2222)=14*sqrt(97);

(P1111+P1112+P1121+P1122-(P1211+P1212+P1221+P1222))^2+(P2111+P2112+P2121+P2122-(P2211+P2212+P2221+P2222))^2=59170;

(P1111+P1112+P1121+P1122-(P1211+P1212+P1221+P1222))^2-(P2111+P2112+P2121+P2122-(P2211+P2212+P2221+P2222))^2=-2376*sqrt(97);

(P1111+P1112-P1121-P1122)^2+(P1211+P1212-P1221-P1222)^2+(P2111+P2112-P2121-P2122)^2+(P2211+P2212-P2221-P2222)^2=18430;

(P1111+P1112-P1121-P1122)^2+(P1211+P1212-P1221-P1222)^2-(P2111+P2112-P2121-P2122)^2-(P2211+P2212-P2221-P2222)^2=-896*sqrt(97);

((P1111+P1112-P1121-P1122)^2-(P1211+P1212-P1221-P1222)^2)^2+((P2111+P2112-P2121-P2122)^2-(P2211+P2212-P2221-P2222)^2)^2=169285370;

((P1111+P1112-P1121-P1122)^2-(P1211+P1212-P1221-P1222)^2)^2-((P2111+P2112-P2121-P2122)^2-(P2211+P2212-P2221-P2222)^2)^2=-17177248*sqrt(97);

(P1111-P1112)^2+(P1121-P1122)^2+(P1211-P1212)^2+(P1221-P1222)^2+(P2111-P2112)^2+(P2121-P2122)^2+(P2211-P2212)^2+(P2221-P2222)^2=19594;

(P1111-P1112)^2+(P1121-P1122)^2+(P1211-P1212)^2+(P1221-P1222)^2-(P2111-P2112)^2-(P2121-P2122)^2-(P2211-P2212)^2-(P2221-P2222)^2=1444*sqrt(97);

((P1111-P1112)^2+(P1121-P1122)^2-(P1211-P1212)^2-(P1221-P1222)^2)^2+((P2111-P2112)^2+(P2121-P2122)^2-(P2211-P2212)^2-(P2221-P2222)^2)^2=270830402;

((P1111-P1112)^2+(P1121-P1122)^2-(P1211-P1212)^2-(P1221-P1222)^2)^2-((P2111-P2112)^2+(P2121-P2122)^2-(P2211-P2212)^2-(P2221-P2222)^2)^2=26799176*sqrt(97);

((P1111-P1112)^2-(P1121-P1122)^2)^2+((P1211-P1212)^2-(P1221-P1222)^2)^2+((P2111-P2112)^2-(P2121-P2122)^2)^2+((P2211-P2212)^2-(P2221-P2222)^2)^2=38112270;

((P1111-P1112)^2-(P1121-P1122)^2)^2+((P1211-P1212)^2-(P1221-P1222)^2)^2-((P2111-P2112)^2-(P2121-P2122)^2)^2-((P2211-P2212)^2-(P2221-P2222)^2)^2=3419416*sqrt(97);

(((P1111-P1112)^2-(P1121-P1122)^2)^2-((P1211-P1212)^2-(P1221-P1222)^2)^2)^2+(((P2111-P2112)^2-(P2121-P2122)^2)^2-((P2211-P2212)^2-(P2221-P2222)^2)^2)^2=1290460012022938;

(((P1111-P1112)^2-(P1121-P1122)^2)^2-((P1211-P1212)^2-(P1221-P1222)^2)^2)^2-(((P2111-P2112)^2-(P2121-P2122)^2)^2-((P2211-P2212)^2-(P2221-P2222)^2)^2)^2=130070552851536*sqrt(97).

?

P1111=(194+7*sqrt(97)+sqrt(29585-1188*sqrt(97))-sqrt(18430-896*sqrt(97)+(7918+796*sqrt(97))*sqrt(55193-5604*sqrt(97)))+2*sqrt(9797+722*sqrt(97)-(31280-3181*sqrt(97))*sqrt(55193+5604*sqrt(97))-sqrt(38112270+3419416*sqrt(97)-(73079212-7441986*sqrt(97))*sqrt(55193+5604*sqrt(97)))))/8;

P1112=(194+7*sqrt(97)+sqrt(29585-1188*sqrt(97))-sqrt(18430-896*sqrt(97)+(7918+796*sqrt(97))*sqrt(55193-5604*sqrt(97)))-2*sqrt(9797+722*sqrt(97)-(31280-3181*sqrt(97))*sqrt(55193+5604*sqrt(97))-sqrt(38112270+3419416*sqrt(97)-(73079212-7441986*sqrt(97))*sqrt(55193+5604*sqrt(97)))))/8;

P1121=(194+7*sqrt(97)+sqrt(29585-1188*sqrt(97))+sqrt(18430-896*sqrt(97)+(7918+796*sqrt(97))*sqrt(55193-5604*sqrt(97)))+2*sqrt(9797+722*sqrt(97)-(31280-3181*sqrt(97))*sqrt(55193+5604*sqrt(97))+sqrt(38112270+3419416*sqrt(97)-(73079212-7441986*sqrt(97))*sqrt(55193+5604*sqrt(97)))))/8;

P1122=(194+7*sqrt(97)+sqrt(29585-1188*sqrt(97))+sqrt(18430-896*sqrt(97)+(7918+796*sqrt(97))*sqrt(55193-5604*sqrt(97)))-2*sqrt(9797+722*sqrt(97)-(31280-3181*sqrt(97))*sqrt(55193+5604*sqrt(97))+sqrt(38112270+3419416*sqrt(97)-(73079212-7441986*sqrt(97))*sqrt(55193+5604*sqrt(97)))))/8;

P1211=(194+7*sqrt(97)-sqrt(29585-1188*sqrt(97))+sqrt(18430-896*sqrt(97)-(7918+796*sqrt(97))*sqrt(55193-5604*sqrt(97)))-2*sqrt(9797+722*sqrt(97)+(31280-3181*sqrt(97))*sqrt(55193+5604*sqrt(97))+sqrt(38112270+3419416*sqrt(97)+(73079212-7441986*sqrt(97))*sqrt(55193+5604*sqrt(97)))))/8;

P1212=(194+7*sqrt(97)-sqrt(29585-1188*sqrt(97))+sqrt(18430-896*sqrt(97)-(7918+796*sqrt(97))*sqrt(55193-5604*sqrt(97)))+2*sqrt(9797+722*sqrt(97)+(31280-3181*sqrt(97))*sqrt(55193+5604*sqrt(97))+sqrt(38112270+3419416*sqrt(97)+(73079212-7441986*sqrt(97))*sqrt(55193+5604*sqrt(97)))))/8;

P1221=(194+7*sqrt(97)-sqrt(29585-1188*sqrt(97))-sqrt(18430-896*sqrt(97)-(7918+796*sqrt(97))*sqrt(55193-5604*sqrt(97)))-2*sqrt(9797+722*sqrt(97)+(31280-3181*sqrt(97))*sqrt(55193+5604*sqrt(97))-sqrt(38112270+3419416*sqrt(97)+(73079212-7441986*sqrt(97))*sqrt(55193+5604*sqrt(97)))))/8;

P1222=(194+7*sqrt(97)-sqrt(29585-1188*sqrt(97))-sqrt(18430-896*sqrt(97)-(7918+796*sqrt(97))*sqrt(55193-5604*sqrt(97)))+2*sqrt(9797+722*sqrt(97)+(31280-3181*sqrt(97))*sqrt(55193+5604*sqrt(97))-sqrt(38112270+3419416*sqrt(97)+(73079212-7441986*sqrt(97))*sqrt(55193+5604*sqrt(97)))))/8;

P2111=(194-7*sqrt(97)-sqrt(29585+1188*sqrt(97))+sqrt(18430+896*sqrt(97)-(7918-796*sqrt(97))*sqrt(55193+5604*sqrt(97)))+2*sqrt(9797-722*sqrt(97)-(31280+3181*sqrt(97))*sqrt(55193-5604*sqrt(97))-sqrt(38112270-3419416*sqrt(97)-(73079212+7441986*sqrt(97))*sqrt(55193-5604*sqrt(97)))))/8;

P2112=(194-7*sqrt(97)-sqrt(29585+1188*sqrt(97))+sqrt(18430+896*sqrt(97)-(7918-796*sqrt(97))*sqrt(55193+5604*sqrt(97)))-2*sqrt(9797-722*sqrt(97)-(31280+3181*sqrt(97))*sqrt(55193-5604*sqrt(97))-sqrt(38112270-3419416*sqrt(97)-(73079212+7441986*sqrt(97))*sqrt(55193-5604*sqrt(97)))))/8;

P2121=(194-7*sqrt(97)-sqrt(29585+1188*sqrt(97))-sqrt(18430+896*sqrt(97)-(7918-796*sqrt(97))*sqrt(55193+5604*sqrt(97)))+2*sqrt(9797-722*sqrt(97)-(31280+3181*sqrt(97))*sqrt(55193-5604*sqrt(97))+sqrt(38112270-3419416*sqrt(97)-(73079212+7441986*sqrt(97))*sqrt(55193-5604*sqrt(97)))))/8;

P2122=(194-7*sqrt(97)-sqrt(29585+1188*sqrt(97))-sqrt(18430+896*sqrt(97)-(7918-796*sqrt(97))*sqrt(55193+5604*sqrt(97)))-2*sqrt(9797-722*sqrt(97)-(31280+3181*sqrt(97))*sqrt(55193-5604*sqrt(97))+sqrt(38112270-3419416*sqrt(97)-(73079212+7441986*sqrt(97))*sqrt(55193-5604*sqrt(97)))))/8;

P2211=(194-7*sqrt(97)+sqrt(29585+1188*sqrt(97))-sqrt(18430+896*sqrt(97)+(7918-796*sqrt(97))*sqrt(55193+5604*sqrt(97)))+2*sqrt(9797-722*sqrt(97)+(31280+3181*sqrt(97))*sqrt(55193-5604*sqrt(97))-sqrt(38112270-3419416*sqrt(97)+(73079212+7441986*sqrt(97))*sqrt(55193-5604*sqrt(97)))))/8;

P2212=(194-7*sqrt(97)+sqrt(29585+1188*sqrt(97))-sqrt(18430+896*sqrt(97)+(7918-796*sqrt(97))*sqrt(55193+5604*sqrt(97)))-2*sqrt(9797-722*sqrt(97)+(31280+3181*sqrt(97))*sqrt(55193-5604*sqrt(97))-sqrt(38112270-3419416*sqrt(97)+(73079212+7441986*sqrt(97))*sqrt(55193-5604*sqrt(97)))))/8;

P2221=(194-7*sqrt(97)+sqrt(29585+1188*sqrt(97))+sqrt(18430+896*sqrt(97)+(7918-796*sqrt(97))*sqrt(55193+5604*sqrt(97)))+2*sqrt(9797-722*sqrt(97)+(31280+3181*sqrt(97))*sqrt(55193-5604*sqrt(97))+sqrt(38112270-3419416*sqrt(97)+(73079212+7441986*sqrt(97))*sqrt(55193-5604*sqrt(97)))))/8;

P2222=(194-7*sqrt(97)+sqrt(29585+1188*sqrt(97))+sqrt(18430+896*sqrt(97)+(7918-796*sqrt(97))*sqrt(55193+5604*sqrt(97)))-2*sqrt(9797-722*sqrt(97)+(31280+3181*sqrt(97))*sqrt(55193-5604*sqrt(97))+sqrt(38112270-3419416*sqrt(97)+(73079212+7441986*sqrt(97))*sqrt(55193-5604*sqrt(97)))))/8;

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V.三次根號內的虛部，可在A、B、C所屬數(shù)域內開根號，最后為了方便，有的參數(shù)要變號。

Q1111=sqrt(A1111^2*B1111^2-27*C1111^2+18*A1111*B1111*C1111-4*A1111^3*C1111-4*B1111^3);

Q1112=sqrt(A1112^2*B1112^2-27*C1112^2+18*A1112*B1112*C1112-4*A1112^3*C1112-4*B1112^3);

Q1121=sqrt(A1121^2*B1121^2-27*C1121^2+18*A1121*B1121*C1121-4*A1121^3*C1121-4*B1121^3);

Q1122=sqrt(A1122^2*B1122^2-27*C1122^2+18*A1122*B1122*C1122-4*A1122^3*C1122-4*B1122^3);

Q1211=-sqrt(A1211^2*B1211^2-27*C1211^2+18*A1211*B1211*C1211-4*A1211^3*C1211-4*B1211^3);

Q1212=sqrt(A1212^2*B1212^2-27*C1212^2+18*A1212*B1212*C1212-4*A1212^3*C1212-4*B1212^3);

Q1221=sqrt(A1221^2*B1221^2-27*C1221^2+18*A1221*B1221*C1221-4*A1221^3*C1221-4*B1221^3);

Q1222=-sqrt(A1222^2*B1222^2-27*C1222^2+18*A1222*B1222*C1222-4*A1222^3*C1222-4*B1222^3);

Q2111=-sqrt(A2111^2*B2111^2-27*C2111^2+18*A2111*B2111*C2111-4*A2111^3*C2111-4*B2111^3);

Q2112=-sqrt(A2112^2*B2112^2-27*C2112^2+18*A2112*B2112*C2112-4*A2112^3*C2112-4*B2112^3);

Q2121=sqrt(A2121^2*B2121^2-27*C2121^2+18*A2121*B2121*C2121-4*A2121^3*C2121-4*B2121^3);

Q2122=sqrt(A2122^2*B2122^2-27*C2122^2+18*A2122*B2122*C2122-4*A2122^3*C2122-4*B2122^3);

Q2211=-sqrt(A2211^2*B2211^2-27*C2211^2+18*A2211*B2211*C2211-4*A2211^3*C2211-4*B2211^3);

Q2212=-sqrt(A2212^2*B2212^2-27*C2212^2+18*A2212*B2212*C2212-4*A2212^3*C2212-4*B2212^3);

Q2221=-sqrt(A2221^2*B2221^2-27*C2221^2+18*A2221*B2221*C2221-4*A2221^3*C2221-4*B2221^3);

Q2222=sqrt(A2222^2*B2222^2-27*C2222^2+18*A2222*B2222*C2222-4*A2222^3*C2222-4*B2222^3);

Q1111 + Q1112 + Q1121 + Q1122 + Q1211 + Q1212 + Q1221 + Q1222 + Q2111 + Q2112 + Q2121 + Q2122 + Q2211 + Q2212 + Q2221 + Q2222 =0;

Q1111 + Q1112 + Q1121 + Q1122 + Q1211 + Q1212 + Q1221 + Q1222 - ( Q2111 + Q2112 + Q2121 + Q2122 + Q2211 + Q2212 + Q2221 + Q2222 ) = 2*sqrt(97);

(Q1111 + Q1112 + Q1121 + Q1122 - Q1211 - Q1212 - Q1221 - Q1222)^2 + ( Q2111 + Q2112 + Q2121 + Q2122 - Q2211 - Q2212 - Q2221 - Q2222 )^2=194;

((Q1111 + Q1112 + Q1121 + Q1122 - Q1211 - Q1212 - Q1221 - Q1222)^2 - ( Q2111 + Q2112 + Q2121 + Q2122 - Q2211 - Q2212 - Q2221 - Q2222 )^2)=-8*sqrt(97);

(Q1111 + Q1112 - Q1121 - Q1122)^2 + (Q1211 + Q1212 - Q1221 - Q1222)^2 + (Q2111 + Q2112 - Q2121 - Q2122)^2 + (Q2211 + Q2212 - Q2221 - Q2222)^2 =194;

((Q1111 + Q1112 - Q1121 - Q1122)^2 + (Q1211 + Q1212 - Q1221 - Q1222)^2 - (Q2111 + Q2112 - Q2121 - Q2122)^2 - (Q2211 + Q2212 - Q2221 - Q2222)^2)=12*sqrt(97);

((Q1111 + Q1112 - Q1121 - Q1122)^2 - (Q1211 + Q1212 - Q1221 - Q1222)^2)^2 + ((Q2111 + Q2112 - Q2121 - Q2122)^2 - (Q2211 + Q2212 - Q2221 - Q2222)^2)^2=12610?;

(((Q1111 + Q1112 - Q1121 - Q1122)^2 - (Q1211 + Q1212 - Q1221 - Q1222)^2)^2 - ((Q2111 + Q2112 - Q2121 - Q2122)^2 - (Q2211 + Q2212 - Q2221 - Q2222)^2)^2)=1272*sqrt(97).

(Q1111-Q1112)^2+(Q1121-Q1122)^2+(Q1211-Q1212)^2+(Q1221-Q1222)^2+(Q2111-Q2112)^2+(Q2121-Q2122)^2+(Q2211-Q2212)^2+(Q2221-Q2222)^2=194;

(((Q1111-Q1112)^2+(Q1121-Q1122)^2+(Q1211-Q1212)^2+(Q1221-Q1222)^2)-((Q2111-Q2112)^2+(Q2121-Q2122)^2+(Q2211-Q2212)^2+(Q2221-Q2222)^2))=4*sqrt(97);

((Q1111-Q1112)^2+(Q1121-Q1122)^2-(Q1211-Q1212)^2-(Q1221-Q1222)^2)^2+((Q2111-Q2112)^2+(Q2121-Q2122)^2-(Q2211-Q2212)^2-(Q2221-Q2222)^2)^2=14162;

(((Q1111-Q1112)^2+(Q1121-Q1122)^2-(Q1211-Q1212)^2-(Q1221-Q1222)^2)^2-((Q2111-Q2112)^2+(Q2121-Q2122)^2-(Q2211-Q2212)^2-(Q2221-Q2222)^2)^2)/sqrt(97)=424;

((Q1111-Q1112)^2-(Q1121-Q1122)^2)^2+((Q1211-Q1212)^2-(Q1221-Q1222)^2)^2+((Q2111-Q2112)^2-(Q2121-Q2122)^2)^2+((Q2211-Q2212)^2-(Q2221-Q2222)^2)^2 =2910;

(((Q1111-Q1112)^2-(Q1121-Q1122)^2)^2+((Q1211-Q1212)^2-(Q1221-Q1222)^2)^2-((Q2111-Q2112)^2-(Q2121-Q2122)^2)^2-((Q2211-Q2212)^2-(Q2221-Q2222)^2)^2) =?248*sqrt(97);

(((Q1111-Q1112)^2-(Q1121-Q1122)^2)^2-((Q1211-Q1212)^2-(Q1221-Q1222)^2)^2)^2+(((Q2111-Q2112)^2-(Q2121-Q2122)^2)^2-((Q2211-Q2212)^2-(Q2221-Q2222)^2)^2)^2=6095674;

((((Q1111-Q1112)^2-(Q1121-Q1122)^2)^2-((Q1211-Q1212)^2-(Q1221-Q1222)^2)^2)^2-(((Q2111-Q2112)^2-(Q2121-Q2122)^2)^2-((Q2211-Q2212)^2-(Q2221-Q2222)^2)^2)^2)=608208*sqrt(97);

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Q1111=(sqrt(97)+sqrt(97-4*sqrt(97))-sqrt(194+12*sqrt(97)-2*sqrt(6305+636*sqrt(97)))+2*sqrt(97+2*sqrt(97)-sqrt(7081+212*sqrt(97))-sqrt(2910+248*sqrt(97)-2*sqrt(3047837+304104*sqrt(97)))))/8;

Q1112=(sqrt(97)+sqrt(97-4*sqrt(97))-sqrt(194+12*sqrt(97)-2*sqrt(6305+636*sqrt(97)))-2*sqrt(97+2*sqrt(97)-sqrt(7081+212*sqrt(97))-sqrt(2910+248*sqrt(97)-2*sqrt(3047837+304104*sqrt(97)))))/8;

Q1121=(sqrt(97)+sqrt(97-4*sqrt(97))+sqrt(194+12*sqrt(97)-2*sqrt(6305+636*sqrt(97)))-2*sqrt(97+2*sqrt(97)-sqrt(7081+212*sqrt(97))+sqrt(2910+248*sqrt(97)-2*sqrt(3047837+304104*sqrt(97)))))/8;

Q1122=(sqrt(97)+sqrt(97-4*sqrt(97))+sqrt(194+12*sqrt(97)-2*sqrt(6305+636*sqrt(97)))+2*sqrt(97+2*sqrt(97)-sqrt(7081+212*sqrt(97))+sqrt(2910+248*sqrt(97)-2*sqrt(3047837+304104*sqrt(97)))))/8;

Q1211=(sqrt(97)-sqrt(97-4*sqrt(97))+sqrt(194+12*sqrt(97)+2*sqrt(6305+636*sqrt(97)))-2*sqrt(97+2*sqrt(97)+sqrt(7081+212*sqrt(97))+sqrt(2910+248*sqrt(97)+2*sqrt(3047837+304104*sqrt(97)))))/8;

Q1212=(sqrt(97)-sqrt(97-4*sqrt(97))+sqrt(194+12*sqrt(97)+2*sqrt(6305+636*sqrt(97)))+2*sqrt(97+2*sqrt(97)+sqrt(7081+212*sqrt(97))+sqrt(2910+248*sqrt(97)+2*sqrt(3047837+304104*sqrt(97)))))/8;

Q1221=(sqrt(97)-sqrt(97-4*sqrt(97))-sqrt(194+12*sqrt(97)+2*sqrt(6305+636*sqrt(97)))+2*sqrt(97+2*sqrt(97)+sqrt(7081+212*sqrt(97))-sqrt(2910+248*sqrt(97)+2*sqrt(3047837+304104*sqrt(97)))))/8;

Q1222=(sqrt(97)-sqrt(97-4*sqrt(97))-sqrt(194+12*sqrt(97)+2*sqrt(6305+636*sqrt(97)))-2*sqrt(97+2*sqrt(97)+sqrt(7081+212*sqrt(97))-sqrt(2910+248*sqrt(97)+2*sqrt(3047837+304104*sqrt(97)))))/8;

Q2111=(-sqrt(97)+sqrt(97+4*sqrt(97))-sqrt(194-12*sqrt(97)+2*sqrt(6305-636*sqrt(97)))+2*sqrt(97-2*sqrt(97)-sqrt(7081-212*sqrt(97))-sqrt(2910-248*sqrt(97)-2*sqrt(3047837-304104*sqrt(97)))))/8;

Q2112=(-sqrt(97)+sqrt(97+4*sqrt(97))-sqrt(194-12*sqrt(97)+2*sqrt(6305-636*sqrt(97)))-2*sqrt(97-2*sqrt(97)-sqrt(7081-212*sqrt(97))-sqrt(2910-248*sqrt(97)-2*sqrt(3047837-304104*sqrt(97)))))/8;

Q2121=(-sqrt(97)+sqrt(97+4*sqrt(97))+sqrt(194-12*sqrt(97)+2*sqrt(6305-636*sqrt(97)))-2*sqrt(97-2*sqrt(97)-sqrt(7081-212*sqrt(97))+sqrt(2910-248*sqrt(97)-2*sqrt(3047837-304104*sqrt(97)))))/8;

Q2122=(-sqrt(97)+sqrt(97+4*sqrt(97))+sqrt(194-12*sqrt(97)+2*sqrt(6305-636*sqrt(97)))+2*sqrt(97-2*sqrt(97)-sqrt(7081-212*sqrt(97))+sqrt(2910-248*sqrt(97)-2*sqrt(3047837-304104*sqrt(97)))))/8;

Q2211=(-sqrt(97)-sqrt(97+4*sqrt(97))-sqrt(194-12*sqrt(97)-2*sqrt(6305-636*sqrt(97)))-2*sqrt(97-2*sqrt(97)+sqrt(7081-212*sqrt(97))+sqrt(2910-248*sqrt(97)+2*sqrt(3047837-304104*sqrt(97)))))/8;

Q2212=(-sqrt(97)-sqrt(97+4*sqrt(97))-sqrt(194-12*sqrt(97)-2*sqrt(6305-636*sqrt(97)))+2*sqrt(97-2*sqrt(97)+sqrt(7081-212*sqrt(97))+sqrt(2910-248*sqrt(97)+2*sqrt(3047837-304104*sqrt(97)))))/8;

Q2221=(-sqrt(97)-sqrt(97+4*sqrt(97))+sqrt(194-12*sqrt(97)-2*sqrt(6305-636*sqrt(97)))-2*sqrt(97-2*sqrt(97)+sqrt(7081-212*sqrt(97))-sqrt(2910-248*sqrt(97)+2*sqrt(3047837-304104*sqrt(97)))))/8;

Q2222=(-sqrt(97)-sqrt(97+4*sqrt(97))+sqrt(194-12*sqrt(97)-2*sqrt(6305-636*sqrt(97)))+2*sqrt(97-2*sqrt(97)+sqrt(7081-212*sqrt(97))-sqrt(2910-248*sqrt(97)+2*sqrt(3047837-304104*sqrt(97)))))/8.

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cos(2*k*pi/97)=(A+f1*((P+Q*j)/2)^(1/3)+f2*((P+Q*j)/2)^(1/3))/6.其中A, P, R是有16個下標只用加減乘除平方根號表示的實數(shù)，下標一致且與正整數(shù)k值相關，三個k值對應一個A, P, Q。f1，f2是三次單位根（包含1）且f1*f2=1，確定A, P, Q可知道((P+sqrt(27)*Q*j)/2)^1/3的輻角和模長，輻角可以加或減120度，使得((P+Q*j)/2)^1/3的模在實軸的投影有三個值，這三種情況分別對應同一A, P, Q情形下3個不同的k值。例如

cos(2*pi/97)=(-1+sqrt(97)-sqrt(194-18*sqrt(97))+2*sqrt(97-5*sqrt(97)+sqrt(10282-1034*sqrt(97)))-2*sqrt(194+14*sqrt(97)-2*sqrt(3298+334*sqrt(97))+4*sqrt(2037+199*sqrt(97)-sqrt(6977210+708198*sqrt(97))))+4*(776+28*sqrt(97)+4*sqrt(29585-1188*sqrt(97))-4*sqrt(18430-896*sqrt(97)+(7918+796*sqrt(97))*sqrt(55193-5604*sqrt(97)))+8*sqrt(9797+722*sqrt(97)-(31280-3181*sqrt(97))*sqrt(55193+5604*sqrt(97))-sqrt(38112270+3419416*sqrt(97)-(73079212-7441986*sqrt(97))*sqrt(55193+5604*sqrt(97))))+12*sqrt(3)*j*(sqrt(97)+sqrt(97-4*sqrt(97))-sqrt(194+12*sqrt(97)-2*sqrt(6305+636*sqrt(97)))+2*sqrt(97+2*sqrt(97)-sqrt(7081+212*sqrt(97))-sqrt(2910+248*sqrt(97)-2*sqrt(3047837+304104*sqrt(97))))))^(1/3)+4*(776+28*sqrt(97)+4*sqrt(29585-1188*sqrt(97))-4*sqrt(18430-896*sqrt(97)+(7918+796*sqrt(97))*sqrt(55193-5604*sqrt(97)))+8*sqrt(9797+722*sqrt(97)-(31280-3181*sqrt(97))*sqrt(55193+5604*sqrt(97))-sqrt(38112270+3419416*sqrt(97)-(73079212-7441986*sqrt(97))*sqrt(55193+5604*sqrt(97))))-12*sqrt(3)*j*(sqrt(97)+sqrt(97-4*sqrt(97))-sqrt(194+12*sqrt(97)-2*sqrt(6305+636*sqrt(97)))+2*sqrt(97+2*sqrt(97)-sqrt(7081+212*sqrt(97))-sqrt(2910+248*sqrt(97)-2*sqrt(3047837+304104*sqrt(97))))))^(1/3))/96;

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cos(70*pi/97)=(-1+sqrt(97)-sqrt(194-18*sqrt(97))+2*sqrt(97-5*sqrt(97)+sqrt(10282-1034*sqrt(97)))-2*sqrt(194+14*sqrt(97)-2*sqrt(3298+334*sqrt(97))+4*sqrt(2037+199*sqrt(97)-sqrt(6977210+708198*sqrt(97))))-(2+2*sqrt(-3))*(776+28*sqrt(97)+4*sqrt(29585-1188*sqrt(97))-4*sqrt(18430-896*sqrt(97)+(7918+796*sqrt(97))*sqrt(55193-5604*sqrt(97)))+8*sqrt(9797+722*sqrt(97)-(31280-3181*sqrt(97))*sqrt(55193+5604*sqrt(97))-sqrt(38112270+3419416*sqrt(97)-(73079212-7441986*sqrt(97))*sqrt(55193+5604*sqrt(97))))+12*sqrt(3)*j*(sqrt(97)+sqrt(97-4*sqrt(97))-sqrt(194+12*sqrt(97)-2*sqrt(6305+636*sqrt(97)))+2*sqrt(97+2*sqrt(97)-sqrt(7081+212*sqrt(97))-sqrt(2910+248*sqrt(97)-2*sqrt(3047837+304104*sqrt(97))))))^(1/3)-(2-2*sqrt(-3))*(776+28*sqrt(97)+4*sqrt(29585-1188*sqrt(97))-4*sqrt(18430-896*sqrt(97)+(7918+796*sqrt(97))*sqrt(55193-5604*sqrt(97)))+8*sqrt(9797+722*sqrt(97)-(31280-3181*sqrt(97))*sqrt(55193+5604*sqrt(97))-sqrt(38112270+3419416*sqrt(97)-(73079212-7441986*sqrt(97))*sqrt(55193+5604*sqrt(97))))-12*sqrt(3)*j*(sqrt(97)+sqrt(97-4*sqrt(97))-sqrt(194+12*sqrt(97)-2*sqrt(6305+636*sqrt(97)))+2*sqrt(97+2*sqrt(97)-sqrt(7081+212*sqrt(97))-sqrt(2910+248*sqrt(97)-2*sqrt(3047837+304104*sqrt(97))))))^(1/3))/96;

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cos(122*pi/97)=(-1+sqrt(97)-sqrt(194-18*sqrt(97))+2*sqrt(97-5*sqrt(97)+sqrt(10282-1034*sqrt(97)))-2*sqrt(194+14*sqrt(97)-2*sqrt(3298+334*sqrt(97))+4*sqrt(2037+199*sqrt(97)-sqrt(6977210+708198*sqrt(97))))-(2-2*sqrt(-3))*(776+28*sqrt(97)+4*sqrt(29585-1188*sqrt(97))-4*sqrt(18430-896*sqrt(97)+(7918+796*sqrt(97))*sqrt(55193-5604*sqrt(97)))+8*sqrt(9797+722*sqrt(97)-(31280-3181*sqrt(97))*sqrt(55193+5604*sqrt(97))-sqrt(38112270+3419416*sqrt(97)-(73079212-7441986*sqrt(97))*sqrt(55193+5604*sqrt(97))))+12*sqrt(3)*j*(sqrt(97)+sqrt(97-4*sqrt(97))-sqrt(194+12*sqrt(97)-2*sqrt(6305+636*sqrt(97)))+2*sqrt(97+2*sqrt(97)-sqrt(7081+212*sqrt(97))-sqrt(2910+248*sqrt(97)-2*sqrt(3047837+304104*sqrt(97))))))^(1/3)-(2+2*sqrt(-3))*(776+28*sqrt(97)+4*sqrt(29585-1188*sqrt(97))-4*sqrt(18430-896*sqrt(97)+(7918+796*sqrt(97))*sqrt(55193-5604*sqrt(97)))+8*sqrt(9797+722*sqrt(97)-(31280-3181*sqrt(97))*sqrt(55193+5604*sqrt(97))-sqrt(38112270+3419416*sqrt(97)-(73079212-7441986*sqrt(97))*sqrt(55193+5604*sqrt(97))))-12*sqrt(3)*j*(sqrt(97)+sqrt(97-4*sqrt(97))-sqrt(194+12*sqrt(97)-2*sqrt(6305+636*sqrt(97)))+2*sqrt(97+2*sqrt(97)-sqrt(7081+212*sqrt(97))-sqrt(2910+248*sqrt(97)-2*sqrt(3047837+304104*sqrt(97))))))^(1/3))/96;

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3.?97次單位根

exp(2kpj/97)=cos(2kp/97)+jsin(2kp/97)，例如：

exp(2pj/97)=(-1+sqrt(97)-sqrt(194-18*sqrt(97))+2*sqrt(97-5*sqrt(97)+sqrt(10282-1034*sqrt(97)))-2*sqrt(194+14*sqrt(97)-2*sqrt(3298+334*sqrt(97))+4*sqrt(2037+199*sqrt(97)-sqrt(6977210+708198*sqrt(97))))+4*(776+28*sqrt(97)+4*sqrt(29585-1188*sqrt(97))-4*sqrt(18430-896*sqrt(97)+(7918+796*sqrt(97))*sqrt(55193-5604*sqrt(97)))+8*sqrt(9797+722*sqrt(97)-(31280-3181*sqrt(97))*sqrt(55193+5604*sqrt(97))-sqrt(38112270+3419416*sqrt(97)-(73079212-7441986*sqrt(97))*sqrt(55193+5604*sqrt(97))))+12*sqrt(3)*j*(sqrt(97)+sqrt(97-4*sqrt(97))-sqrt(194+12*sqrt(97)-2*sqrt(6305+636*sqrt(97)))+2*sqrt(97+2*sqrt(97)-sqrt(7081+212*sqrt(97))-sqrt(2910+248*sqrt(97)-2*sqrt(3047837+304104*sqrt(97))))))^(1/3)+4*(776+28*sqrt(97)+4*sqrt(29585-1188*sqrt(97))-4*sqrt(18430-896*sqrt(97)+(7918+796*sqrt(97))*sqrt(55193-5604*sqrt(97)))+8*sqrt(9797+722*sqrt(97)-(31280-3181*sqrt(97))*sqrt(55193+5604*sqrt(97))-sqrt(38112270+3419416*sqrt(97)-(73079212-7441986*sqrt(97))*sqrt(55193+5604*sqrt(97))))-12*sqrt(3)*j*(sqrt(97)+sqrt(97-4*sqrt(97))-sqrt(194+12*sqrt(97)-2*sqrt(6305+636*sqrt(97)))+2*sqrt(97+2*sqrt(97)-sqrt(7081+212*sqrt(97))-sqrt(2910+248*sqrt(97)-2*sqrt(3047837+304104*sqrt(97))))))^(1/3)+4*j*(sqrt(97-5*sqrt(97)-sqrt(970+22*sqrt(97))-2*sqrt(873-77*sqrt(97)-sqrt(472778-47274*sqrt(97)))-2*sqrt(2)*sqrt(873-41*sqrt(97)-sqrt(464242-25154*sqrt(97))-2*sqrt(155685-11417*sqrt(97)-sqrt(26752018970-2526439674*sqrt(97)))))-(1+sqrt(-3))*(-sqrt(19594-584*sqrt(97)+(170918+17360*sqrt(97))*sqrt(55193-5604*sqrt(97))-2*sqrt(45563034-4579628*sqrt(97)-(1642146+141656*sqrt(97))*sqrt(55193-5604*sqrt(97)))-4*sqrt(27041757-931126*sqrt(97)+(301229863+30594976*sqrt(97))*sqrt(55193-5604*sqrt(97))-sqrt(596661915089958-59813233865024*sqrt(97)+(125926845956502+13142350715116*sqrt(97))*sqrt(55193-5604*sqrt(97)))))+j*3*sqrt(1746+108*sqrt(97)-6*sqrt(1261-88*sqrt(97))+6*sqrt(64602+5044*sqrt(97)-2*sqrt(1335982649+132853668*sqrt(97)))-12*sqrt(34241+3062*sqrt(97)-sqrt(993516001+100534468*sqrt(97))-sqrt(2991680790+301724080*sqrt(97)+(243925700-26563002*sqrt(97))*sqrt(55193+5604*sqrt(97))))))^(1/3)-(1-sqrt(-3))*(-sqrt(19594-584*sqrt(97)+(170918+17360*sqrt(97))*sqrt(55193-5604*sqrt(97))-2*sqrt(45563034-4579628*sqrt(97)-(1642146+141656*sqrt(97))*sqrt(55193-5604*sqrt(97)))-4*sqrt(27041757-931126*sqrt(97)+(301229863+30594976*sqrt(97))*sqrt(55193-5604*sqrt(97))-sqrt(596661915089958-59813233865024*sqrt(97)+(125926845956502+13142350715116*sqrt(97))*sqrt(55193-5604*sqrt(97)))))-j*3*sqrt(1746+108*sqrt(97)-6*sqrt(1261-88*sqrt(97))+6*sqrt(64602+5044*sqrt(97)-2*sqrt(1335982649+132853668*sqrt(97)))-12*sqrt(34241+3062*sqrt(97)-sqrt(993516001+100534468*sqrt(97))-sqrt(2991680790+301724080*sqrt(97)+(243925700-26563002*sqrt(97))*sqrt(55193+5604*sqrt(97))))))^(1/3)))/96