73邊形-(二)
第二節(jié).求解cos(2*k*pi/73)，利用2次和3次剩余劃分
I.分組
A111=2*(cos(2*pi/73)+cos(16*pi/73)+cos(128*pi/73));
A112=2*(cos(4*pi/73)+cos(32*pi/73)+cos(110*pi/73));
A113=2*(cos(8*pi/73)+cos(64*pi/73)+cos(74*pi/73));
A121=2*(cos(92*pi/73)+cos(6*pi/73)+cos(48*pi/73));
A122=2*(cos(38*pi/73)+cos(12*pi/73)+cos(96*pi/73));
A123=2*(cos(76*pi/73)+cos(24*pi/73)+cos(46*pi/73));
A211=2*(cos(20*pi/73)+cos(14*pi/73)+cos(112*pi/73));
A212=2*(cos(40*pi/73)+cos(28*pi/73)+cos(78*pi/73));
A213=2*(cos(80*pi/73)+cos(56*pi/73)+cos(10*pi/73));
A221=2*(cos(44*pi/73)+cos(60*pi/73)+cos(42*pi/73));
A222=2*(cos(58*pi/73)+cos(26*pi/73)+cos(62*pi/73));
A223=2*(cos(30*pi/73)+cos(94*pi/73)+cos(22*pi/73));
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B111=4*(cos(2*pi/73)*cos(16*pi/73)+cos(16*pi/73)*cos(128*pi/73)+cos(128*pi/73)*cos(2*pi/73));
B112=4*(cos(4*pi/73)*cos(32*pi/73)+cos(32*pi/73)*cos(110*pi/73)+cos(110*pi/73)*cos(4*pi/73));
B113=4*(cos(8*pi/73)*cos(64*pi/73)+cos(64*pi/73)*cos(74*pi/73)+cos(74*pi/73)*cos(8*pi/73));
B121=4*(cos(92*pi/73)*cos(6*pi/73)+cos(6*pi/73)*cos(48*pi/73)+cos(48*pi/73)*cos(92*pi/73));
B122=4*(cos(38*pi/73)*cos(12*pi/73)+cos(12*pi/73)*cos(96*pi/73)+cos(96*pi/73)*cos(38*pi/73));
B123=4*(cos(76*pi/73)*cos(24*pi/73)+cos(24*pi/73)*cos(46*pi/73)+cos(46*pi/73)*cos(76*pi/73));
B211=4*(cos(20*pi/73)*cos(14*pi/73)+cos(14*pi/73)*cos(112*pi/73)+cos(112*pi/73)*cos(20*pi/73));
B212=4*(cos(40*pi/73)*cos(28*pi/73)+cos(28*pi/73)*cos(78*pi/73)+cos(78*pi/73)*cos(40*pi/73));
B213=4*(cos(80*pi/73)*cos(56*pi/73)+cos(56*pi/73)*cos(10*pi/73)+cos(10*pi/73)*cos(80*pi/73));
B221=4*(cos(44*pi/73)*cos(60*pi/73)+cos(60*pi/73)*cos(42*pi/73)+cos(42*pi/73)*cos(44*pi/73));
B222=4*(cos(58*pi/73)*cos(26*pi/73)+cos(26*pi/73)*cos(62*pi/73)+cos(62*pi/73)*cos(58*pi/73));
B223=4*(cos(30*pi/73)*cos(94*pi/73)+cos(94*pi/73)*cos(22*pi/73)+cos(22*pi/73)*cos(30*pi/73));
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C111=8*(cos(2*pi/73)*cos(16*pi/73)*cos(128*pi/73));
C112=8*(cos(4*pi/73)*cos(32*pi/73)*cos(110*pi/73));
C113=8*(cos(8*pi/73)*cos(64*pi/73)*cos(74*pi/73));
C121=8*(cos(92*pi/73)*cos(6*pi/73)*cos(48*pi/73));
C122=8*(cos(38*pi/73)*cos(12*pi/73)*cos(96*pi/73));
C123=8*(cos(76*pi/73)*cos(24*pi/73)*cos(46*pi/73));
C211=8*(cos(20*pi/73)*cos(14*pi/73)*cos(112*pi/73));
C212=8*(cos(40*pi/73)*cos(28*pi/73)*cos(78*pi/73));
C213=8*(cos(80*pi/73)*cos(56*pi/73)*cos(10*pi/73));
C221=8*(cos(44*pi/73)*cos(60*pi/73)*cos(42*pi/73));
C222=8*(cos(58*pi/73)*cos(26*pi/73)*cos(62*pi/73));
C223=8*(cos(30*pi/73)*cos(94*pi/73)*cos(22*pi/73));
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II.A、B、C值
II.1 A
(A111+A112+A113) + (A121+A122+A123) = (-1+sqrt(73))/2;
(A211+A212+A113) + (A221+A222+A223) = (-1-sqrt(73))/2;
((A111+A112+A113) - (A121+A122+A123))^2 + ((A211+A212+A213) - (A221+A222+A223))^2
=3*sqrt(73);
X11=(A111+A112+A113)=(-1+sqrt(73)+sqrt(146+6*sqrt(73)))/4;
X12=(A121+A122+A123)=(-1+sqrt(73)-sqrt(146+6*sqrt(73)))/4;
X21=(A211+A212+A213)=(-1-sqrt(73)+sqrt(146-6*sqrt(73)))/4;
X22=(A221+A222+A223)=(-1-sqrt(73)-sqrt(146-6*sqrt(73)))/4;
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A111*A112+A112*A113+A113*A111 + A121*A122+A122*A123+A123*A121=-3;
A211*A212+A212*A213+A213*A211 + A221*A222+A222*A223+A223*A221=-3;
(A111*A112+A112*A113+A113*A111 -(A121*A122+A122*A123+A123*A121))^2+(A211*A212+A212*A213+A213*A211 -( A221*A222+A222*A223+A223*A221))^2=146;
(A111*A112+A112*A113+A113*A111 -(A121*A122+A122*A123+A123*A121))^2-(A211*A212+A212*A213+A213*A211 -( A221*A222+A222*A223+A223*A221))^2=-16*sqrt(73);
Y11=(A111*A112+A112*A113+A113*A111)=(-3-sqrt(73-8*sqrt(73)))/2;
Y12=(A121*A122+A122*A123+A123*A121)=(-3+sqrt(73-8*sqrt(73)))/2;
Y21=(A211*A212+A212*A213+A213*A211)=(-3-sqrt(73+8*sqrt(73)))/2;
Y22=(A221*A222+A222*A223+A223*A221)=(-3+sqrt(73+8*sqrt(73)))/2;
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A111*A112*A113+A121*A122*A123=-6-2*sqrt(73);
A211*A212*A213+A221*A222*A223=-6+2*sqrt(73);
((A111*A112*A113)-(A121*A122*A123))^2+((A211*A212*A213)-(A221*A222*A223))^2=584;
((A111*A112*A113)-(A121*A122*A123))^2-((A211*A212*A213)-(A221*A222*A223))^2=64*sqrt(73);
Z11=(A111*A112*A113)=-3-sqrt(73)-sqrt(73+8*sqrt(73));
Z12=(A121*A122*A123)=-3-sqrt(73)+sqrt(73+8*sqrt(73));
Z21=(A211*A212*A213)=-3+sqrt(73)+sqrt(73-8*sqrt(73));
Z22=(A221*A222*A223)=-3+sqrt(73)-sqrt(73-8*sqrt(73));
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P11=2*X11^3-9*X11*Y11+27*Z11;
P12=2*X12^3-9*X12*Y12+27*Z12;
P21=2*X21^3-9*X21*Y21+27*Z21;
P22=2*X22^3-9*X22*Y22+27*Z22;
P11+P12+P21+P22=73; P11+P12-P21-P22=-55*sqrt(73);
(P11-P12)^2+(P21-P22)^2=57889; ?(P11-P12)^2-(P21-P22)^2=1461*sqrt(73);
P11=(73-55*sqrt(73)-sqrt(115778+2922*sqrt(73)))/4;
P12=(73-55*sqrt(73)+sqrt(115778+2922*sqrt(73)))/4;
P21=(73+55*sqrt(73)+sqrt(115778-2922*sqrt(73)))/4;
P22=(73+55*sqrt(73)-sqrt(115778-2922*sqrt(73)))/4;
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Q11=sqrt(X11^2*Y11^2-27*Z11^2+18*X11*Y11*Z11-4*X11^3*Z11-4*Y11^3);
Q12=-sqrt(X12^2*Y12^2-27*Z12^2+18*X12*Y12*Z12-4*X12^3*Z12-4*Y12^3);
Q21=sqrt(X21^2*Y21^2-27*Z21^2+18*X21*Y21*Z21-4*X21^3*Z21-4*Y21^3);
Q22=-sqrt(X22^2*Y22^2-27*Z22^2+18*X22*Y22*Z22-4*X22^3*Z22-4*Y22^3);
Q11+Q12+Q21+Q22=73; ???Q11+Q12-Q21-Q22=9*sqrt(73);
(Q11-Q12)^2+(Q21-Q22)^2=6497; ?(Q11-Q12)^2-(Q21-Q22)^2=757*sqrt(73);
Q11=(73+9*sqrt(73)+sqrt(12994+1514*sqrt(73)))/4;
Q12=(73+9*sqrt(73)-sqrt(12994+1514*sqrt(73)))/4;
Q21=(73-9*sqrt(73)+sqrt(12994-1514*sqrt(73)))/4;
Q22=(73-9*sqrt(73)-sqrt(12994-1514*sqrt(73)))/4;
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A111=(-1+sqrt(73)+sqrt(146+6*sqrt(73))+2*(73-55*sqrt(73)-sqrt(115778+2922*sqrt(73))+3*sqrt(-3)*(73+9*sqrt(73)+sqrt(12994+1514*sqrt(73))))^(1/3)+2*(73-55*sqrt(73)-sqrt(115778+2922*sqrt(73))-3*sqrt(-3)*(73+9*sqrt(73)+sqrt(12994+1514*sqrt(73))))^(1/3))/12;
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A112=(-1+sqrt(73)+sqrt(146+6*sqrt(73))+2*w2*(73-55*sqrt(73)-sqrt(115778+2922*sqrt(73))+3*sqrt(-3)*(73+9*sqrt(73)+sqrt(12994+1514*sqrt(73))))^(1/3)+2*w1*(73-55*sqrt(73)-sqrt(115778+2922*sqrt(73))-3*sqrt(-3)*(73+9*sqrt(73)+sqrt(12994+1514*sqrt(73))))^(1/3))/12;
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A113=(-1+sqrt(73)+sqrt(146+6*sqrt(73))+2*w1*(73-55*sqrt(73)-sqrt(115778+2922*sqrt(73))+3*sqrt(-3)*(73+9*sqrt(73)+sqrt(12994+1514*sqrt(73))))^(1/3)+2*w2*(73-55*sqrt(73)-sqrt(115778+2922*sqrt(73))-3*sqrt(-3)*(73+9*sqrt(73)+sqrt(12994+1514*sqrt(73))))^(1/3))/12;
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A121=(-1+sqrt(73)-sqrt(146+6*sqrt(73))+2*w1*(73-55*sqrt(73)+sqrt(115778+2922*sqrt(73))+3*sqrt(-3)*(73+9*sqrt(73)-sqrt(12994+1514*sqrt(73))))^(1/3)+2*w2*(73-55*sqrt(73)+sqrt(115778+2922*sqrt(73))-3*sqrt(-3)*(73+9*sqrt(73)-sqrt(12994+1514*sqrt(73))))^(1/3))/12;
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A122=(-1+sqrt(73)-sqrt(146+6*sqrt(73))+2*(73-55*sqrt(73)+sqrt(115778+2922*sqrt(73))+3*sqrt(-3)*(73+9*sqrt(73)-sqrt(12994+1514*sqrt(73))))^(1/3)+2*(73-55*sqrt(73)+sqrt(115778+2922*sqrt(73))-3*sqrt(-3)*(73+9*sqrt(73)-sqrt(12994+1514*sqrt(73))))^(1/3))/12;
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A123=(-1+sqrt(73)-sqrt(146+6*sqrt(73))+2*w2*(73-55*sqrt(73)+sqrt(115778+2922*sqrt(73))+3*sqrt(-3)*(73+9*sqrt(73)-sqrt(12994+1514*sqrt(73))))^(1/3)+2*w1*(73-55*sqrt(73)+sqrt(115778+2922*sqrt(73))-3*sqrt(-3)*(73+9*sqrt(73)-sqrt(12994+1514*sqrt(73))))^(1/3))/12;
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A211=(-1-sqrt(73)+sqrt(146-6*sqrt(73))+2*(73+55*sqrt(73)+sqrt(115778-2922*sqrt(73))+3*sqrt(-3)*(73-9*sqrt(73)+sqrt(12994-1514*sqrt(73))))^(1/3)+2*(73+55*sqrt(73)+sqrt(115778-2922*sqrt(73))-3*sqrt(-3)*(73-9*sqrt(73)+sqrt(12994-1514*sqrt(73))))^(1/3))/12;
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A212=(-1-sqrt(73)+sqrt(146-6*sqrt(73))+2*w2*(73+55*sqrt(73)+sqrt(115778-2922*sqrt(73))+3*sqrt(-3)*(73-9*sqrt(73)+sqrt(12994-1514*sqrt(73))))^(1/3)+2*w1*(73+55*sqrt(73)+sqrt(115778-2922*sqrt(73))-3*sqrt(-3)*(73-9*sqrt(73)+sqrt(12994-1514*sqrt(73))))^(1/3))/12;
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A213=(-1-sqrt(73)+sqrt(146-6*sqrt(73))+2*w1*(73+55*sqrt(73)+sqrt(115778-2922*sqrt(73))+3*sqrt(-3)*(73-9*sqrt(73)+sqrt(12994-1514*sqrt(73))))^(1/3)+2*w2*(73+55*sqrt(73)+sqrt(115778-2922*sqrt(73))-3*sqrt(-3)*(73-9*sqrt(73)+sqrt(12994-1514*sqrt(73))))^(1/3))/12;
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A221=(-1-sqrt(73)-sqrt(146-6*sqrt(73))+2*w2*(73+55*sqrt(73)-sqrt(115778-2922*sqrt(73))+3*sqrt(-3)*(73-9*sqrt(73)-sqrt(12994-1514*sqrt(73))))^(1/3)+2*w1*(73+55*sqrt(73)-sqrt(115778-2922*sqrt(73))-3*sqrt(-3)*(73-9*sqrt(73)-sqrt(12994-1514*sqrt(73))))^(1/3))/12;
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A222=(-1-sqrt(73)-sqrt(146-6*sqrt(73))+2*w1*(73+55*sqrt(73)-sqrt(115778-2922*sqrt(73))+3*sqrt(-3)*(73-9*sqrt(73)-sqrt(12994-1514*sqrt(73))))^(1/3)+2*w2*(73+55*sqrt(73)-sqrt(115778-2922*sqrt(73))-3*sqrt(-3)*(73-9*sqrt(73)-sqrt(12994-1514*sqrt(73))))^(1/3))/12;
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A223=(-1-sqrt(73)-sqrt(146-6*sqrt(73))+2*(73+55*sqrt(73)-sqrt(115778-2922*sqrt(73))+3*sqrt(-3)*(73-9*sqrt(73)-sqrt(12994-1514*sqrt(73))))^(1/3)+2*(73+55*sqrt(73)-sqrt(115778-2922*sqrt(73))-3*sqrt(-3)*(73-9*sqrt(73)-sqrt(12994-1514*sqrt(73))))^(1/3))/12;
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II.2 C
C111=2+A112; C112=2+A113; C113=2+A111; C121=2+A122; C122=2+A123; C123=2+A121;
C211=2+A212; C212=2+A213; C213=2+A211; C221=2+A222; C222=2+A223; C223=2+A221;
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II.3 B
B111+B112+B113+B121+B122+B123 + B211+B212+B213+B221+B222+B223 =-2;
B111+B112+B113+B121+B122+B123 - (B211+B212+B213+B221+B222+B223) =0;
(B111+B112+B113-(B121+B122+B123))^2+(B211+B212+B213-(B221+B222+B223))^2=146;
(B111+B112+B113-(B121+B122+B123))^2-(B211+B212+B213-(B221+B222+B223))^2=16*sqrt(73);
R11=B111+B112+B113=(-1+sqrt(73+8*sqrt(73)))/2;
R12=B121+B122+B123=(-1-sqrt(73+8*sqrt(73)))/2;
R21=B211+B212+B213=(-1-sqrt(73-8*sqrt(73)))/2;
R22=B221+B222+B223=(-1+sqrt(73-8*sqrt(73)))/2;
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B111*B112+B112*B113+B113*B111 + B121*B122+B122*B123+B123*B121 = -12;
B211*B212+B212*B213+B213*B211 + B221*B222+B222*B223+B223*B221 = -12;
(B111*B112+B112*B113+B113*B111-(B121*B122+B122*B123+B123*B121))^2+(B211*B212+B212*B213+B213*B211 -( B221*B222+B222*B223+B223*B221))^2=1460;
(B111*B112+B112*B113+B113*B111-(B121*B122+B122*B123+B123*B121))^2-(B211*B212+B212*B213+B213*B211 -( B221*B222+B222*B223+B223*B221))^2=164*sqrt(73);
S11=B111*B112+B112*B113+B113*B111=-6+sqrt(730+82*sqrt(73))/2;
S12=B121*B122+B122*B123+B123*B121=-6-sqrt(730+82*sqrt(73))/2;
S21=B211*B212+B212*B213+B213*B211=-6-sqrt(730-82*sqrt(73))/2;
S22=B221*B222+B222*B223+B223*B221=-6+sqrt(730-82*sqrt(73))/2;
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B111*B112*B113 + B121*B122*B123 + B211*B212*B213 + B221*B222*B223=-23;
B111*B112*B113 + B121*B122*B123 -(B211*B212*B213 + B221*B222*B223)=-5*sqrt(73);
(B111*B112*B113 -(B121*B122*B123))^2 + (B211*B212*B213 -(B221*B222*B223))^2=365;
(B111*B112*B113 -(B121*B122*B123))^2 - (B211*B212*B213 -(B221*B222*B223))^2=23*sqrt(73);
T11=B111*B112*B113=(-23-5*sqrt(73)-sqrt(730+46*sqrt(73)))/4;
T12=B121*B122*B123=(-23-5*sqrt(73)+sqrt(730+46*sqrt(73)))/4;
T21=B211*B212*B213=(-23+5*sqrt(73)+sqrt(730-46*sqrt(73)))/4;
T22=B221*B222*B223=(-23+5*sqrt(73)-sqrt(730-46*sqrt(73)))/4;
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K11=2*R11^3-9*R11*S11+27*T11; ?K12=2*R12^3-9*R12*S12+27*T12;
K21=2*R21^3-9*R21*S21+27*T21; ?K22=2*R22^3-9*R22*S22+27*T22;
K11+K12 + K21+K22=1022; K11+K12 - K21-K22=84*sqrt(73);
(K11-K12)^2 + (K21-K22)^2 = 779786; ?(K11-K12)^2 - (K21-K22)^2 = 88984*sqrt(73);
K11=7*(73+6*sqrt(73)+sqrt(7957+908*sqrt(73)))/2;
K12=7*(73+6*sqrt(73)-sqrt(7957+908*sqrt(73)))/2;
K21=7*(73-6*sqrt(73)+sqrt(7957-908*sqrt(73)))/2;
K22=7*(73-6*sqrt(73)-sqrt(7957-908*sqrt(73)))/2;
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L11=sqrt(R11^2*S11^2-27*T11^2-4*R11^3*T11-4*S11^3+18*R11*S11*T11);
L12=-sqrt(R12^2*S12^2-27*T12^2-4*R12^3*T12-4*S12^3+18*R12*S12*T12);
L21=sqrt(R21^2*S21^2-27*T21^2-4*R21^3*T21-4*S21^3+18*R21*S21*T21);
L22=sqrt(R22^2*S22^2-27*T22^2-4*R22^3*T22-4*S22^3+18*R22*S22*T22);
L11+L12+L21+L22=438; ??L11+L12-L21-L22=36*sqrt(73);
(L11-L12)^2+(L21-L22)^2=143226; ??(L11-L12)^2-(L21-L22)^2=16344*sqrt(73);
L11=3/7*K11; L12=3/7*K12; L21=3/7*K21; L22=3/7*K22;
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B111=(-1+sqrt(73+8*sqrt(73))+((14+18*sqrt(-3))*(73+6*sqrt(73)+sqrt(7957+908*sqrt(73))))^(1/3)+((14-18*sqrt(-3))*(73+6*sqrt(73)+sqrt(7957+908*sqrt(73))))^(1/3))/6;
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B112=(-1+sqrt(73+8*sqrt(73))+w2*((14+18*sqrt(-3))*(73+6*sqrt(73)+sqrt(7957+908*sqrt(73))))^(1/3)+w1*((14-18*sqrt(-3))*(73+6*sqrt(73)+sqrt(7957+908*sqrt(73))))^(1/3))/6;
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B113=(-1+sqrt(73+8*sqrt(73))+w1*((14+18*sqrt(-3))*(73+6*sqrt(73)+sqrt(7957+908*sqrt(73))))^(1/3)+w2*((14-18*sqrt(-3))*(73+6*sqrt(73)+sqrt(7957+908*sqrt(73))))^(1/3))/6;
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B121=(-1-sqrt(73+8*sqrt(73))+w2*((14+18*sqrt(-3))*(73+6*sqrt(73)-sqrt(7957+908*sqrt(73))))^(1/3)+w1*((14-18*sqrt(-3))*(73+6*sqrt(73)-sqrt(7957+908*sqrt(73))))^(1/3))/6;
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B122=(-1-sqrt(73+8*sqrt(73))+w1*((14+18*sqrt(-3))*(73+6*sqrt(73)-sqrt(7957+908*sqrt(73))))^(1/3)+w2*((14-18*sqrt(-3))*(73+6*sqrt(73)-sqrt(7957+908*sqrt(73))))^(1/3))/6;
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B123=(-1-sqrt(73+8*sqrt(73))+((14+18*sqrt(-3))*(73+6*sqrt(73)-sqrt(7957+908*sqrt(73))))^(1/3)+((14-18*sqrt(-3))*(73+6*sqrt(73)-sqrt(7957+908*sqrt(73))))^(1/3))/6;
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B211=(-1-sqrt(73-8*sqrt(73))+((14+18*sqrt(-3))*(73-6*sqrt(73)+sqrt(7957-908*sqrt(73))))^(1/3)+((14-18*sqrt(-3))*(73-6*sqrt(73)+sqrt(7957-908*sqrt(73))))^(1/3))/6;
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B212=(-1-sqrt(73-8*sqrt(73))+w2*((14+18*sqrt(-3))*(73-6*sqrt(73)+sqrt(7957-908*sqrt(73))))^(1/3)+w1*((14-18*sqrt(-3))*(73-6*sqrt(73)+sqrt(7957-908*sqrt(73))))^(1/3))/6;
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B213=(-1-sqrt(73-8*sqrt(73))+w1*((14+18*sqrt(-3))*(73-6*sqrt(73)+sqrt(7957-908*sqrt(73))))^(1/3)+w2*((14-18*sqrt(-3))*(73-6*sqrt(73)+sqrt(7957-908*sqrt(73))))^(1/3))/6;
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B221=(-1+sqrt(73-8*sqrt(73))+((14+18*sqrt(-3))*(73-6*sqrt(73)-sqrt(7957-908*sqrt(73))))^(1/3)+((14-18*sqrt(-3))*(73-6*sqrt(73)-sqrt(7957-908*sqrt(73))))^(1/3))/6;
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B222=(-1+sqrt(73-8*sqrt(73))+w2*((14+18*sqrt(-3))*(73-6*sqrt(73)-sqrt(7957-908*sqrt(73))))^(1/3)+w1*((14-18*sqrt(-3))*(73-6*sqrt(73)-sqrt(7957-908*sqrt(73))))^(1/3))/6;
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B223=(-1+sqrt(73-8*sqrt(73))+w1*((14+18*sqrt(-3))*(73-6*sqrt(73)-sqrt(7957-908*sqrt(73))))^(1/3)+w2*((14-18*sqrt(-3))*(73-6*sqrt(73)-sqrt(7957-908*sqrt(73))))^(1/3))/6;
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III.三次根號內(nèi)的數(shù)據(jù)
2*實部：M=2*A^3-9*A*B+27*C
2*虛部/sqrt(-27)：N=±sqrt(A^2*B^2-27*C^2+18*A*B*C-4*A^3*C-4*B^3);
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(1)M
M111=2*A111^3-9*A111*B111+27*C111;
M112=2*A112^3-9*A112*B112+27*C112;
M113=2*A113^3-9*A113*B113+27*C113;
M121=2*A121^3-9*A121*B121+27*C121;
M122=2*A122^3-9*A122*B122+27*C122;
M123=2*A123^3-9*A123*B123+27*C123;
M211=2*A211^3-9*A211*B211+27*C211;
M212=2*A212^3-9*A212*B212+27*C212;
M213=2*A213^3-9*A213*B213+27*C213;
M221=2*A221^3-9*A221*B221+27*C221;
M222=2*A222^3-9*A222*B222+27*C222;
M223=2*A223^3-9*A223*B223+27*C223;
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(M111+M112+M113) + (M121+M122+M123) + (M211+M212+M213) + (M221+M222+M223)=292;
(M111+M112+M113) + (M121+M122+M123) -?(M211+M212+M213) -?(M221+M222+M223)=14*sqrt(73);
((M111+M112+M113)-(M121+M122+M123))^2+((M211+M212+M213)-(M221+M222+M223))^2=4234;
((M111+M112+M113)-(M121+M122+M123))^2-((M211+M212+M213)-(M221+M222+M223))^2=-216*sqrt(73);
a11=(M111+M112+M113)=(146+7*sqrt(73)+sqrt(2117-108*sqrt(73)))/2;
a12=(M121+M122+M123)=(146+7*sqrt(73)-sqrt(2117-108*sqrt(73)))/2;
a21=(M211+M212+M213)=(146-7*sqrt(73)+sqrt(2117+108*sqrt(73)))/2;
a22=(M221+M222+M223)=(146-7*sqrt(73)-sqrt(2117+108*sqrt(73)))/2;
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M111*M112+M112*M113+M113*M111+M121*M122+M122*M123+M123*M121+M211*M212+M212*M213+M213*M211+M221*M222+M222*M223+M223*M221=1314;
M111*M112+M112*M113+M113*M111+M121*M122+M122*M123+M123*M121-(M211*M212+M212*M213+M213*M211+M221*M222+M222*M223+M223*M221)=540*sqrt(73);
(M111*M112+M112*M113+M113*M111-(M121*M122+M122*M123+M123*M121))^2+(M211*M212+M212*M213+M213*M211-(M221*M222+M222*M223+M223*M221))^2=837602;
(M111*M112+M112*M113+M113*M111-(M121*M122+M122*M123+M123*M121))^2-(M211*M212+M212*M213+M213*M211-(M221*M222+M222*M223+M223*M221))^2=25712*sqrt(73);
b11=M111*M112+M112*M113+M113*M111=(657+270*sqrt(73)+sqrt(418801+12856*sqrt(73)))/2;
b12=M121*M122+M122*M123+M123*M121=(657+270*sqrt(73)-sqrt(418801+12856*sqrt(73)))/2;
b21=M211*M212+M212*M213+M213*M211=(657-270*sqrt(73)+sqrt(418801-12856*sqrt(73)))/2;
b22=M221*M222+M222*M223+M223*M221=(657-270*sqrt(73)-sqrt(418801-12856*sqrt(73)))/2;
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(M111*M112*M113) + (M121*M122*M123) + (M211*M212*M213) + (M221*M222*M223) =16206;
(M111*M112*M113) + (M121*M122*M123) - (M211*M212*M213) - (M221*M222*M223) =898*sqrt(73);
((M111*M112*M113)-(M121*M122*M123))^2+((M211*M212*M213)-(M221*M222*M223))^2=132978260;
((M111*M112*M113)-(M121*M122*M123))^2-((M211*M212*M213)-(M221*M222*M223))^2=15072964*sqrt(73);
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c11=M111*M112*M113=(8103+449*sqrt(73)-sqrt(66489130+7536482*sqrt(73)))/2;
c12=M121*M122*M123=(8103+449*sqrt(73)+sqrt(66489130+7536482*sqrt(73)))/2;
c21=M211*M212*M213=(8103-449*sqrt(73)+sqrt(66489130-7536482*sqrt(73)))/2;
c22=M221*M222*M223=(8103-449*sqrt(73)-sqrt(66489130-7536482*sqrt(73)))/2;
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實部內(nèi)的三次根號內(nèi)待定系數(shù)f、g
f11=2*a11^3-9*a11*b11+27*c11;
f12=2*a12^3-9*a12*b12+27*c12;
f21=2*a21^3-9*a21*b21+27*c21;
f22=2*a22^3-9*a22*b22+27*c22;
f11+f12+f21+f22=4024052;
f11+f12-f21-f22=94996*sqrt(73);
(f11-f12)^2+(f21-f22)^2=6349429320904;
(f11-f12)^2-(f21-f22)^2=308771360256;
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f11=1006013+23749*sqrt(73)+(5388569-629766*sqrt(73))*sqrt(9125+1068*sqrt(73));
f12=1006013+23749*sqrt(73)-(5388569-629766*sqrt(73))*sqrt(9125+1068*sqrt(73));
f21=1006013-23749*sqrt(73)+(5388569+629766*sqrt(73))*sqrt(9125-1068*sqrt(73));
f22=1006013-23749*sqrt(73)-(5388569+629766*sqrt(73))*sqrt(9125-1068*sqrt(73));
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虛部：g11=sqrt(a11^2*b11^2-27*c11^2+18*a11*b11*c11-4*a11^3*c11-4*b11^3);
g12=-sqrt(a12^2*b12^2-27*c12^2+18*a12*b12*c12-4*a12^3*c12-4*b12^3);
g21=-sqrt(a21^2*b21^2-27*c21^2+18*a21*b21*c21-4*a21^3*c21-4*b21^3);
g22=sqrt(a22^2*b22^2-27*c22^2+18*a22*b22*c22-4*a22^3*c22-4*b22^3);
g11+g12 + g21+g22 =65116;
g11+g12 - g21-g22 =15924*sqrt(73);
(g11-g12)^2 + (g21-g22)^2=18603591560;
(g11-g12)^2 - (g21-g22)^2=779994496*sqrt(73);
g11=16279+3981*sqrt(73)-(305203-35770*sqrt(73))*sqrt(9125+1068*sqrt(73));
g12=16279+3981*sqrt(73)+(305203-35770*sqrt(73))*sqrt(9125+1068*sqrt(73));
g21=16279-3981*sqrt(73)-(305203+35770*sqrt(73))*sqrt(9125-1068*sqrt(73));
g22=16279-3981*sqrt(73)+(305203+35770*sqrt(73))*sqrt(9125-1068*sqrt(73));
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M111/2=(146+7*sqrt(73)+sqrt(2117-108*sqrt(73))+w1*(4024052+94996*sqrt(73)+(21554276-2519064*sqrt(73))*sqrt(9125+1068*sqrt(73))+12*sqrt(-3)*(16279+3981*sqrt(73)-(305203-35770*sqrt(73))*sqrt(9125+1068*sqrt(73))))^(1/3)+w2*(4024052+94996*sqrt(73)+(21554276-2519064*sqrt(73))*sqrt(9125+1068*sqrt(73))-12*sqrt(-3)*(16279+3981*sqrt(73)-(305203-35770*sqrt(73))*sqrt(9125+1068*sqrt(73))))^(1/3))/12;
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M112/2=(146+7*sqrt(73)+sqrt(2117-108*sqrt(73))+w2*(4024052+94996*sqrt(73)+(21554276-2519064*sqrt(73))*sqrt(9125+1068*sqrt(73))+12*sqrt(-3)*(16279+3981*sqrt(73)-(305203-35770*sqrt(73))*sqrt(9125+1068*sqrt(73))))^(1/3)+w1*(4024052+94996*sqrt(73)+(21554276-2519064*sqrt(73))*sqrt(9125+1068*sqrt(73))-12*sqrt(-3)*(16279+3981*sqrt(73)-(305203-35770*sqrt(73))*sqrt(9125+1068*sqrt(73))))^(1/3))/12;
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M113/2=(146+7*sqrt(73)+sqrt(2117-108*sqrt(73))+(4024052+94996*sqrt(73)+(21554276-2519064*sqrt(73))*sqrt(9125+1068*sqrt(73))+12*sqrt(-3)*(16279+3981*sqrt(73)-(305203-35770*sqrt(73))*sqrt(9125+1068*sqrt(73))))^(1/3)+(4024052+94996*sqrt(73)+(21554276-2519064*sqrt(73))*sqrt(9125+1068*sqrt(73))-12*sqrt(-3)*(16279+3981*sqrt(73)-(305203-35770*sqrt(73))*sqrt(9125+1068*sqrt(73))))^(1/3))/12;
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M121/2=(146+7*sqrt(73)-sqrt(2117-108*sqrt(73))+(4024052+94996*sqrt(73)-(21554276-2519064*sqrt(73))*sqrt(9125+1068*sqrt(73))+12*sqrt(-3)*(16279+3981*sqrt(73)+(305203-35770*sqrt(73))*sqrt(9125+1068*sqrt(73))))^(1/3)+(4024052+94996*sqrt(73)-(21554276-2519064*sqrt(73))*sqrt(9125+1068*sqrt(73))-12*sqrt(-3)*(16279+3981*sqrt(73)+(305203-35770*sqrt(73))*sqrt(9125+1068*sqrt(73))))^(1/3))/12;
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M122/2=(146+7*sqrt(73)-sqrt(2117-108*sqrt(73))+w1*(4024052+94996*sqrt(73)-(21554276-2519064*sqrt(73))*sqrt(9125+1068*sqrt(73))+12*sqrt(-3)*(16279+3981*sqrt(73)+(305203-35770*sqrt(73))*sqrt(9125+1068*sqrt(73))))^(1/3)+w2*(4024052+94996*sqrt(73)-(21554276-2519064*sqrt(73))*sqrt(9125+1068*sqrt(73))-12*sqrt(-3)*(16279+3981*sqrt(73)+(305203-35770*sqrt(73))*sqrt(9125+1068*sqrt(73))))^(1/3))/12;
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M123/2=(146+7*sqrt(73)-sqrt(2117-108*sqrt(73))+w2*(4024052+94996*sqrt(73)-(21554276-2519064*sqrt(73))*sqrt(9125+1068*sqrt(73))+12*sqrt(-3)*(16279+3981*sqrt(73)+(305203-35770*sqrt(73))*sqrt(9125+1068*sqrt(73))))^(1/3)+w1*(4024052+94996*sqrt(73)-(21554276-2519064*sqrt(73))*sqrt(9125+1068*sqrt(73))-12*sqrt(-3)*(16279+3981*sqrt(73)+(305203-35770*sqrt(73))*sqrt(9125+1068*sqrt(73))))^(1/3))/12;
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M211/2=(146-7*sqrt(73)+sqrt(2117+108*sqrt(73))+w1*(4024052-94996*sqrt(73)+(21554276+2519064*sqrt(73))*sqrt(9125-1068*sqrt(73))+12*sqrt(-3)*(16279-3981*sqrt(73)-(305203+35770*sqrt(73))*sqrt(9125-1068*sqrt(73))))^(1/3)+w2*(4024052-94996*sqrt(73)+(21554276+2519064*sqrt(73))*sqrt(9125-1068*sqrt(73))-12*sqrt(-3)*(16279-3981*sqrt(73)-(305203+35770*sqrt(73))*sqrt(9125-1068*sqrt(73))))^(1/3))/12;
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M212/2=(146-7*sqrt(73)+sqrt(2117+108*sqrt(73))+w2*(4024052-94996*sqrt(73)+(21554276+2519064*sqrt(73))*sqrt(9125-1068*sqrt(73))+12*sqrt(-3)*(16279-3981*sqrt(73)-(305203+35770*sqrt(73))*sqrt(9125-1068*sqrt(73))))^(1/3)+w1*(4024052-94996*sqrt(73)+(21554276+2519064*sqrt(73))*sqrt(9125-1068*sqrt(73))-12*sqrt(-3)*(16279-3981*sqrt(73)-(305203+35770*sqrt(73))*sqrt(9125-1068*sqrt(73))))^(1/3))/12;
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M213/2=(146-7*sqrt(73)+sqrt(2117+108*sqrt(73))+(4024052-94996*sqrt(73)+(21554276+2519064*sqrt(73))*sqrt(9125-1068*sqrt(73))+12*sqrt(-3)*(16279-3981*sqrt(73)-(305203+35770*sqrt(73))*sqrt(9125-1068*sqrt(73))))^(1/3)+(4024052-94996*sqrt(73)+(21554276+2519064*sqrt(73))*sqrt(9125-1068*sqrt(73))-12*sqrt(-3)*(16279-3981*sqrt(73)-(305203+35770*sqrt(73))*sqrt(9125-1068*sqrt(73))))^(1/3))/12;
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M221/2=(146-7*sqrt(73)-sqrt(2117+108*sqrt(73))+w2*(4024052-94996*sqrt(73)-(21554276+2519064*sqrt(73))*sqrt(9125-1068*sqrt(73))+12*sqrt(-3)*(16279-3981*sqrt(73)+(305203+35770*sqrt(73))*sqrt(9125-1068*sqrt(73))))^(1/3)+w1*(4024052-94996*sqrt(73)-(21554276+2519064*sqrt(73))*sqrt(9125-1068*sqrt(73))-12*sqrt(-3)*(16279-3981*sqrt(73)+(305203+35770*sqrt(73))*sqrt(9125-1068*sqrt(73))))^(1/3))/12;
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M222/2=(146-7*sqrt(73)-sqrt(2117+108*sqrt(73))+(4024052-94996*sqrt(73)-(21554276+2519064*sqrt(73))*sqrt(9125-1068*sqrt(73))+12*sqrt(-3)*(16279-3981*sqrt(73)+(305203+35770*sqrt(73))*sqrt(9125-1068*sqrt(73))))^(1/3)+(4024052-94996*sqrt(73)-(21554276+2519064*sqrt(73))*sqrt(9125-1068*sqrt(73))-12*sqrt(-3)*(16279-3981*sqrt(73)+(305203+35770*sqrt(73))*sqrt(9125-1068*sqrt(73))))^(1/3))/12;
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M223/2=(146-7*sqrt(73)-sqrt(2117+108*sqrt(73))+w1*(4024052-94996*sqrt(73)-(21554276+2519064*sqrt(73))*sqrt(9125-1068*sqrt(73))+12*sqrt(-3)*(16279-3981*sqrt(73)+(305203+35770*sqrt(73))*sqrt(9125-1068*sqrt(73))))^(1/3)+w2*(4024052-94996*sqrt(73)-(21554276+2519064*sqrt(73))*sqrt(9125-1068*sqrt(73))-12*sqrt(-3)*(16279-3981*sqrt(73)+(305203+35770*sqrt(73))*sqrt(9125-1068*sqrt(73))))^(1/3))/12;
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(2)N
N111=sqrt(A111^2*B111^2-27*C111^2+18*A111*B111*C111-4*A111^3*C111-4*B111^3);
N112=sqrt(A112^2*B112^2-27*C112^2+18*A112*B112*C112-4*A112^3*C112-4*B112^3);
N113=sqrt(A113^2*B113^2-27*C113^2+18*A113*B113*C113-4*A113^3*C113-4*B113^3);
N121=sqrt(A121^2*B121^2-27*C121^2+18*A121*B121*C121-4*A121^3*C121-4*B121^3);
N122=-sqrt(A122^2*B122^2-27*C122^2+18*A122*B122*C122-4*A122^3*C122-4*B122^3);
N123=sqrt(A123^2*B123^2-27*C123^2+18*A123*B123*C123-4*A123^3*C123-4*B123^3);
N211=-sqrt(A211^2*B211^2-27*C211^2+18*A211*B211*C211-4*A211^3*C211-4*B211^3);
N212=-sqrt(A212^2*B212^2-27*C212^2+18*A212*B212*C212-4*A212^3*C212-4*B212^3);
N213=-sqrt(A213^2*B213^2-27*C213^2+18*A213*B213*C213-4*A213^3*C213-4*B213^3);
N221=sqrt(A221^2*B221^2-27*C221^2+18*A221*B221*C221-4*A221^3*C221-4*B221^3);
N222=-sqrt(A222^2*B222^2-27*C222^2+18*A222*B222*C222-4*A222^3*C222-4*B222^3);
N223=sqrt(A223^2*B223^2-27*C223^2+18*A223*B223*C223-4*A223^3*C223-4*B223^3);
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(N111+N112+N113)+(N121+N122+N123)=sqrt(73);
(N211+N212+N213)+(N221+N222+N223)=-sqrt(73);
((N111+N112+N113)-(N121+N122+N123))^2+((N211+N212+N213)-(N221+N222+N223))^2=146;
(N111+N112+N113-(N121+N122+N123))^2-(N211+N212+N213-(N221+N222+N223))^2=-16*sqrt(73);
k11=N111+N112+N113=(sqrt(73)-sqrt(73-8*sqrt(73)))/2;
k12=N121+N122+N123=(sqrt(73)+sqrt(73-8*sqrt(73)))/2;
k21=N211+N212+N213=-(sqrt(73)+sqrt(73+8*sqrt(73)))/2;
k22=N221+N222+N223=-(sqrt(73)-sqrt(73+8*sqrt(73)))/2;
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N111*N112+N112*N113+N113*N111+N121*N122+N122*N123+N123*N121+N211*N212+N212*N213+N213*N211+N221*N222+N222*N223+N223*N221=0;
N111*N112+N112*N113+N113*N111+N121*N122+N122*N123+N123*N121= -3*sqrt(73);
(N111*N112+N112*N113+N113*N111-(N121*N122+N122*N123+N123*N121))^2+(N211*N212+N212*N213+N213*N211-(N221*N222+N222*N223+N223*N221))^2=1898;
(N111*N112+N112*N113+N113*N111-(N121*N122+N122*N123+N123*N121))^2-(N211*N212+N212*N213+N213*N211-(N221*N222+N222*N223+N223*N221))^2=-8*sqrt(73);
l11=N111*N112+N112*N113+N113*N111=(-3*sqrt(73)+sqrt(949-4*sqrt(73)))/2;
l12=N121*N122+N122*N123+N123*N121=(-3*sqrt(73)-sqrt(949-4*sqrt(73)))/2;
l21=N211*N212+N212*N213+N213*N211=(3*sqrt(73)+sqrt(949+4*sqrt(73)))/2;
l22=N221*N222+N222*N223+N223*N221=(3*sqrt(73)-sqrt(949+4*sqrt(73)))/2;
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(N111*N112*N113)+(N121*N122*N123)+(N211*N212*N213)+(N221*N222*N223)=-146;
(N111*N112*N113)+(N121*N122*N123)-(N211*N212*N213)-(N221*N222*N223)=-14*sqrt(73);
((N111*N112*N113)-(N121*N122*N123))^2+((N211*N212*N213)-(N221*N222*N223))^2=17812;
((N111*N112*N113)-(N121*N122*N123))^2+((N211*N212*N213)-(N221*N222*N223))^2=2052*sqrt(73);
m11=N111*N112*N113=(-73-7*sqrt(73)+sqrt(8906+1026*sqrt(73)))/2;
m12=N121*N122*N123=(-73-7*sqrt(73)-sqrt(8906+1026*sqrt(73)))/2;
m21=N211*N212*N213=(-73+7*sqrt(73)-sqrt(8906-1026*sqrt(73)))/2;
m22=N221*N222*N223=(-73+7*sqrt(73)+sqrt(8906-1026*sqrt(73)))/2;
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N的待定系數(shù)u、v
u11=2*k11^3-9*k11*l11+27*m11;
u12=2*k12^3-9*k12*l12+27*m12;
u21=2*k21^3-9*k21*l21+27*m21;
u22=2*k22^3-9*k22*l22+27*m22;
u11+u12+u21+u22=-1752;
u11+u12-u21-u22=-248*sqrt(73);
(u11-u12)^2+(u21-u22)^2=3763880;
(u11-u12)^2-(u21-u22)^2=437408*sqrt(73);
u11=-438-62*sqrt(73)+sqrt(470485+54676*sqrt(73));
u12=-438-62*sqrt(73)-sqrt(470485+54676*sqrt(73));
u21=-438+62*sqrt(73)+sqrt(470485-54676*sqrt(73));
u22=-438+62*sqrt(73)-sqrt(470485-54676*sqrt(73));
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v11=-sqrt(k11^2*l11^2-27*m11^2+18*k11*l11*m11-4*k11^3*m11-4*l11^3);
v12=sqrt(k12^2*l12^2-27*m12^2+18*k12*l12*m12-4*k12^3*m12-4*l12^3);
v21=sqrt(k21^2*l21^2-27*m21^2+18*k21*l21*m21-4*k21^3*m21-4*l21^3);
v22=sqrt(k22^2*l22^2-27*m22^2+18*k22*l22*m22-4*k22^3*m22-4*l22^3);
v11+v12+v21+v22=292;
v11+v12-v21-v22=28*sqrt(73);
(v11-v12)^2+(v21-v22)^2=73000;
(v11-v12)^2-(v21-v22)^2=8544*sqrt(73);
v11=(73+7*sqrt(73)-sqrt(9125+1068*sqrt(73)));
v12=(73+7*sqrt(73)+sqrt(9125+1068*sqrt(73)));
v21=(73-7*sqrt(73)-sqrt(9125-1068*sqrt(73)));
v22=(73-7*sqrt(73)+sqrt(9125-1068*sqrt(73)));
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3*sqrt(3)*N111/2=3*sqrt(3)*((sqrt(73)-sqrt(73-8*sqrt(73)))+w2*(-1752-248*sqrt(73)+4*sqrt(470485+54676*sqrt(73))+12*sqrt(3)*j*(73+7*sqrt(73)-sqrt(9125+1068*sqrt(73))))^(1/3)+w1*(-1752-248*sqrt(73)+4*sqrt(470485+54676*sqrt(73))-12*sqrt(3)*j*(73+7*sqrt(73)-sqrt(9125+1068*sqrt(73))))^(1/3))/12;
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3*sqrt(3)*N112/2=3*sqrt(3)*((sqrt(73)-sqrt(73-8*sqrt(73)))+w1*(-1752-248*sqrt(73)+4*sqrt(470485+54676*sqrt(73))+12*sqrt(3)*j*(73+7*sqrt(73)-sqrt(9125+1068*sqrt(73))))^(1/3)+w2*(-1752-248*sqrt(73)+4*sqrt(470485+54676*sqrt(73))-12*sqrt(3)*j*(73+7*sqrt(73)-sqrt(9125+1068*sqrt(73))))^(1/3))/12;
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3*sqrt(3)*N113/2=3*sqrt(3)*((sqrt(73)-sqrt(73-8*sqrt(73)))+(-1752-248*sqrt(73)+4*sqrt(470485+54676*sqrt(73))+12*sqrt(3)*j*(73+7*sqrt(73)-sqrt(9125+1068*sqrt(73))))^(1/3)+(-1752-248*sqrt(73)+4*sqrt(470485+54676*sqrt(73))-12*sqrt(3)*j*(73+7*sqrt(73)-sqrt(9125+1068*sqrt(73))))^(1/3))/12;
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3*sqrt(3)*N121/2=3*sqrt(3)*((sqrt(73)+sqrt(73-8*sqrt(73)))+w2*(-1752-248*sqrt(73)-4*sqrt(470485+54676*sqrt(73))+12*sqrt(3)*j*(73+7*sqrt(73)+sqrt(9125+1068*sqrt(73))))^(1/3)+w1*(-1752-248*sqrt(73)-4*sqrt(470485+54676*sqrt(73))-12*sqrt(3)*j*(73+7*sqrt(73)+sqrt(9125+1068*sqrt(73))))^(1/3))/12;
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3*sqrt(3)*N122/2=3*sqrt(3)*((sqrt(73)+sqrt(73-8*sqrt(73)))+w1*(-1752-248*sqrt(73)-4*sqrt(470485+54676*sqrt(73))+12*sqrt(3)*j*(73+7*sqrt(73)+sqrt(9125+1068*sqrt(73))))^(1/3)+w2*(-1752-248*sqrt(73)-4*sqrt(470485+54676*sqrt(73))-12*sqrt(3)*j*(73+7*sqrt(73)+sqrt(9125+1068*sqrt(73))))^(1/3))/12;
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3*sqrt(3)*N123/2=3*sqrt(3)*((sqrt(73)+sqrt(73-8*sqrt(73)))+(-1752-248*sqrt(73)-4*sqrt(470485+54676*sqrt(73))+12*sqrt(3)*j*(73+7*sqrt(73)+sqrt(9125+1068*sqrt(73))))^(1/3)+(-1752-248*sqrt(73)-4*sqrt(470485+54676*sqrt(73))-12*sqrt(3)*j*(73+7*sqrt(73)+sqrt(9125+1068*sqrt(73))))^(1/3))/12;
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3*sqrt(3)*N211/2=3*sqrt(3)*((-sqrt(73)-sqrt(73+8*sqrt(73)))+(-1752+248*sqrt(73)+4*sqrt(470485-54676*sqrt(73))+12*sqrt(3)*j*(73-7*sqrt(73)-sqrt(9125-1068*sqrt(73))))^(1/3)+(-1752+248*sqrt(73)+4*sqrt(470485-54676*sqrt(73))-12*sqrt(3)*j*(73-7*sqrt(73)-sqrt(9125-1068*sqrt(73))))^(1/3))/12;
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3*sqrt(3)*N212/2=3*sqrt(3)*((-sqrt(73)-sqrt(73+8*sqrt(73)))+w2*(-1752+248*sqrt(73)+4*sqrt(470485-54676*sqrt(73))+12*sqrt(3)*j*(73-7*sqrt(73)-sqrt(9125-1068*sqrt(73))))^(1/3)+w1*(-1752+248*sqrt(73)+4*sqrt(470485-54676*sqrt(73))-12*sqrt(3)*j*(73-7*sqrt(73)-sqrt(9125-1068*sqrt(73))))^(1/3))/12;
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3*sqrt(3)*N213/2=3*sqrt(3)*((-sqrt(73)-sqrt(73+8*sqrt(73)))+w1*(-1752+248*sqrt(73)+4*sqrt(470485-54676*sqrt(73))+12*sqrt(3)*j*(73-7*sqrt(73)-sqrt(9125-1068*sqrt(73))))^(1/3)+w2*(-1752+248*sqrt(73)+4*sqrt(470485-54676*sqrt(73))-12*sqrt(3)*j*(73-7*sqrt(73)-sqrt(9125-1068*sqrt(73))))^(1/3))/12;
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3*sqrt(3)*N221/2=3*sqrt(3)*((-sqrt(73)+sqrt(73+8*sqrt(73)))+w2*(-1752+248*sqrt(73)-4*sqrt(470485-54676*sqrt(73))+12*sqrt(3)*j*(73-7*sqrt(73)+sqrt(9125-1068*sqrt(73))))^(1/3)+w1*(-1752+248*sqrt(73)-4*sqrt(470485-54676*sqrt(73))-12*sqrt(3)*j*(73-7*sqrt(73)+sqrt(9125-1068*sqrt(73))))^(1/3))/12;
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3*sqrt(3)*N222/2=3*sqrt(3)*((-sqrt(73)+sqrt(73+8*sqrt(73)))+w1*(-1752+248*sqrt(73)-4*sqrt(470485-54676*sqrt(73))+12*sqrt(3)*j*(73-7*sqrt(73)+sqrt(9125-1068*sqrt(73))))^(1/3)+w2*(-1752+248*sqrt(73)-4*sqrt(470485-54676*sqrt(73))-12*sqrt(3)*j*(73-7*sqrt(73)+sqrt(9125-1068*sqrt(73))))^(1/3))/12;
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3*sqrt(3)*N223/2=3*sqrt(3)*((-sqrt(73)+sqrt(73+8*sqrt(73)))+(-1752+248*sqrt(73)-4*sqrt(470485-54676*sqrt(73))+12*sqrt(3)*j*(73-7*sqrt(73)+sqrt(9125-1068*sqrt(73))))^(1/3)+(-1752+248*sqrt(73)-4*sqrt(470485-54676*sqrt(73))-12*sqrt(3)*j*(73-7*sqrt(73)+sqrt(9125-1068*sqrt(73))))^(1/3))/12;
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IV. 最后組裝
cos(2*k*pi/73)的表達式形式是(A+z1*(M/2+N*sqrt(-27)/2)^(1/3)+z2*(M/2+N*sqrt(-27)/2)^(1/3))/6，且A、M、N的下標相同，同一個下標對應(yīng)三個不同的k，任一個k唯一對應(yīng)三次單位根z1、z2且z1*z2=1?？梢宰罱K組合出以下表達式，見下例，染色部分全是實數(shù)。其他類推。
cos(2*pi/73)=(-1+sqrt(73)+sqrt(146+6*sqrt(73))+2*(73-55*sqrt(73)-sqrt(115778+2922*sqrt(73))+3*sqrt(-3)*(73+9*sqrt(73)+sqrt(12994+1514*sqrt(73))))^(1/3)+2*(73-55*sqrt(73)-sqrt(115778+2922*sqrt(73))-3*sqrt(-3)*(73+9*sqrt(73)+sqrt(12994+1514*sqrt(73))))^(1/3)+2*(18*(146+7*sqrt(73)+sqrt(2117-108*sqrt(73))+w1*(4024052+94996*sqrt(73)+(21554276-2519064*sqrt(73))*sqrt(9125+1068*sqrt(73))+12*sqrt(-3)*(16279+3981*sqrt(73)-(305203-35770*sqrt(73))*sqrt(9125+1068*sqrt(73))))^(1/3)+w2*(4024052+94996*sqrt(73)+(21554276-2519064*sqrt(73))*sqrt(9125+1068*sqrt(73))-12*sqrt(-3)*(16279+3981*sqrt(73)-(305203-35770*sqrt(73))*sqrt(9125+1068*sqrt(73))))^(1/3))+54*sqrt(-3)*(sqrt(73)-sqrt(73-8*sqrt(73))+w2*(-1752-248*sqrt(73)+4*sqrt(470485+54676*sqrt(73))+12*sqrt(3)*j*(73+7*sqrt(73)-sqrt(9125+1068*sqrt(73))))^(1/3)+w1*(-1752-248*sqrt(73)+4*sqrt(470485+54676*sqrt(73))-12*sqrt(3)*j*(73+7*sqrt(73)-sqrt(9125+1068*sqrt(73))))^(1/3)))^(1/3)+2*(18*(146+7*sqrt(73)+sqrt(2117-108*sqrt(73))+w1*(4024052+94996*sqrt(73)+(21554276-2519064*sqrt(73))*sqrt(9125+1068*sqrt(73))+12*sqrt(-3)*(16279+3981*sqrt(73)-(305203-35770*sqrt(73))*sqrt(9125+1068*sqrt(73))))^(1/3)+w2*(4024052+94996*sqrt(73)+(21554276-2519064*sqrt(73))*sqrt(9125+1068*sqrt(73))-12*sqrt(-3)*(16279+3981*sqrt(73)-(305203-35770*sqrt(73))*sqrt(9125+1068*sqrt(73))))^(1/3))-54*sqrt(-3)*(sqrt(73)-sqrt(73-8*sqrt(73))+w2*(-1752-248*sqrt(73)+4*sqrt(470485+54676*sqrt(73))+12*sqrt(3)*j*(73+7*sqrt(73)-sqrt(9125+1068*sqrt(73))))^(1/3)+w1*(-1752-248*sqrt(73)+4*sqrt(470485+54676*sqrt(73))-12*sqrt(3)*j*(73+7*sqrt(73)-sqrt(9125+1068*sqrt(73))))^(1/3)))^(1/3))/72
估計值0.9962981749。
最后的彩蛋：73次單位根
