function analy % % input data ns=2; hv=9340.0; % /MHz g.xx=2.003; g.yy=2.003; g.zz=2.003; D.Dvalue=0.205; D.Evalue=0.041; % /cm-1 FLD=analysolution(ns,hv,g,D,0,0,0) FLD=analysolution(ns,hv,g,D,90,0,0) FLD=analysolution(ns,hv,g,D,90,90,0) %%% function FLD=analysolution(ns,hv,g,D,theta,phi,psi) cmmhz=2.99792458e4; fjumhz=1.5091890e27; betae=9.2740154e-24; tensor.g=diag([g.xx,g.yy,g.zz])*betae*fjumhz; tensor.d=diag([-D.Dvalue/3+D.Evalue,-D.Dvalue/3-D.Evalue,2*D.Dvalue/3])*cmmhz; tensor1.g=rotmat(theta*pi/180,phi*pi/180,psi*pi/180,tensor.g); tensor1.d=rotmat(theta*pi/180,phi*pi/180,psi*pi/180,tensor.d); FLD=ef_axis(2*ns+1,hv,tensor1); %%% function FLD=ef_axis(n,hv,tensor) Dxx=tensor.d(1,1)/hv; Dyy=tensor.d(2,2)/hv; Dzz=tensor.d(3,3)/hv; Dv=3*tensor.d(3,3)/2/hv; Ev=(tensor.d(1,1)-tensor.d(2,2))/2/hv; switch n case 2 clear coef; coef(1)=-1; coef(2)=1; FLD2=roots(coef); FLD=sqrt(FLD2')*hv/tensor.g(3,3); case 3 clear coef; coef(1)=-4; coef(2)=9 + 8*Dv^2 - 12*Ev^2; coef(3)=-2*(3 - 3*Dv^2 + 2*Dv^4 - 9*Ev^2 - 8*Dv^2*Ev^2 + 6*Ev^4); coef(4)=-((-1 + Dv - Ev)*(1 + Dv - Ev)*(-1 + Dv + Ev)*(1 + Dv + Ev)*(-1 + 2*Ev)*(1 + 2*Ev)); FLD2=roots(coef); FLD=sqrt(FLD2')*hv/tensor.g(3,3); case 4 clear coef; coef(1)=16; coef(2)=-8*(1 + 4*Dv^2 - 12*Ev^2); coef(3)=(-1 + 4*Dv^2 + 12*Ev^2)^2; FLD21=roots(coef); clear coef; coef(1)=9; coef(2)=-4*(7 + 18*Dv^2 - 18*Ev^2); coef(3)=2*(15 + 4*Dv^2 + 72*Dv^4 - 84*Ev^2 - 144*Dv^2*Ev^2 + 72*Ev^4); coef(4)=-4*(3 - 18*Dv^2 + 40*Dv^4 - 30*Ev^2 + 144*Dv^2*Ev^2 + 72*Ev^4); coef(5)=(-1 + 4*Dv^2 + 12*Ev^2)^2; FLD22=roots(coef); FLD=sqrt([FLD21',FLD22'])*hv/tensor.g(3,3); case 5 clear coef; coef(1)=-256; coef(2)=16*(9 + 128*Dv^2 - 144*Ev^2); coef(3)=-8*(3 - 48*Dv^2 + 512*Dv^4 - 108*Ev^2 + 1920*Dv^2*Ev^2 + 864*Ev^4); coef(4)=(1 + 4*Dv - 12*Ev^2)*(-1 + 4*Dv + 12*Ev^2)*(-1 + 16*Dv^2 + 48*Ev^2); FLD21=roots(coef); clear coef; coef(1)=-4; coef(2)=-((-1 + 6*Ev)*(1 + 6*Ev)); FLD22=roots(coef); clear coef; coef(1)=-9; coef(2)=19 - 42*Dv + 99*Dv^2 - 99*Ev^2; coef(3)=-11 + 52*Dv - 34*Dv^2 - 12*Dv^3 - 171*Dv^4 + 150*Ev^2 - 852*Dv*Ev^2 + 342*Dv^2*Ev^2 - 171*Ev^4; coef(4)=(-1 + 3*Dv - 3*Ev)*(-1 + 3*Dv + 3*Ev)*(-1 + 2*Dv + 3*Dv^2 + 6*Ev - 6*Dv*Ev + 3*Ev^2)* ... (-1 + 2*Dv + 3*Dv^2 - 6*Ev + 6*Dv*Ev + 3*Ev^2); FLD23=roots(coef); clear coef; coef(1)=-9; coef(2)=19 + 42*Dv + 99*Dv^2 - 99*Ev^2; coef(3)=-11 - 52*Dv - 34*Dv^2 + 12*Dv^3 - 171*Dv^4 + 150*Ev^2 + 852*Dv*Ev^2 + 342*Dv^2*Ev^2 - 171*Ev^4; coef(4)=(1 + 3*Dv - 3*Ev)*(1 + 3*Dv + 3*Ev)*(-1 - 2*Dv + 3*Dv^2 - 6*Ev - 6*Dv*Ev + 3*Ev^2)* ... (-1 - 2*Dv + 3*Dv^2 + 6*Ev + 6*Dv*Ev + 3*Ev^2); FLD24=roots(coef); FLD=sqrt([FLD21',FLD22',FLD23',FLD24'])*hv/tensor.g(3,3); case 6 clear coef; coef(1)=65536; coef(2)=-8192*(9 + 176*Dv^2 - 336*Ev^2); coef(3)=256*(129 + 2400*Dv^2 + 40704*Dv^4 - 10080*Ev^2 - 101888*Dv^2*Ev^2 + 174336*Ev^4); coef(4)=-256*(29 + 20*Dv^2 + 11840*Dv^4 + 111616*Dv^6 - 3612*Ev^2 + 11136*Dv^2*Ev^2 - 586752*Dv^4*Ev^2 + ... 133344*Ev^4 - 436736*Dv^2*Ev^4 - 1465856*Ev^6); coef(5)=32*(27 - 760*Dv^2 + 16304*Dv^4 + 28160*Dv^6 + 1144832*Dv^8 - 4872*Ev^2 + 143520*Dv^2*Ev^2 - ... 2118144*Dv^4*Ev^2 - 614400*Dv^6*Ev^2 + 293040*Ev^4 - 8137728*Dv^2*Ev^4 + 76382208*Dv^4*Ev^4 - ... 7031808*Ev^6 + 141328384*Dv^2*Ev^6 + 58994688*Ev^8); coef(6)=-16*(3 - 180*Dv^2 + 2480*Dv^4 + 23360*Dv^6 - 325120*Dv^8 + 1400832*Dv^10 - 756*Ev^2 + ... 42208*Dv^2*Ev^2 - 271424*Dv^4*Ev^2 - 5752832*Dv^6*Ev^2 + 20045824*Dv^8*Ev^2 + 67344*Ev^4 - ... 3353664*Dv^2*Ev^4 + 5125632*Dv^4*Ev^4 + 299900928*Dv^6*Ev^4 - 2686656*Ev^6 + 104272896*Dv^2*Ev^6 + ... 163946496*Dv^4*Ev^6 + 49222656*Ev^8 - 1039925248*Dv^2*Ev^8 - 337182720*Ev^10); coef(7)=(-1 + 56*Dv^2 - 784*Dv^4 + 2304*Dv^6 + 168*Ev^2 - 4704*Dv^2*Ev^2 + 46336*Dv^4*Ev^2 - 7056*Ev^4 + ... 11008*Dv^2*Ev^4 + 87808*Ev^6)^2; FLD21=roots(coef); clear coef; coef(1)=-18225; coef(2)=243*(403 + 3600*Dv^2 - 3600*Ev^2); coef(3)=-108*(2011 + 22824*Dv^2 + 145800*Dv^4 - 39672*Ev^2 - 291600*Dv^2*Ev^2 + 145800*Ev^4); coef(4)=4*(63733 + 516600*Dv^2 + 6799464*Dv^4 + 33825600*Dv^6 - 2139912*Ev^2 - 11737872*Dv^2*Ev^2 - ... 101476800*Dv^4*Ev^2 + 18302760*Ev^4 + 101476800*Dv^2*Ev^4 - 33825600*Ev^6); coef(5)=-2*(84303 + 62384*Dv^2 + 9016560*Dv^4 + 63618048*Dv^6 + 300931200*Dv^8 - 4451088*Ev^2 + ... 12884256*Dv^2*Ev^2 - 298391040*Dv^4*Ev^2 - 1203724800*Dv^6*Ev^2 + 67715568*Ev^4 - ... 191102976*Dv^2*Ev^4 + 1805587200*Dv^4*Ev^4 - 326592000*Ev^6 - 1203724800*Dv^2*Ev^6 + 300931200*Ev^8); coef(6)=2*(30975 - 250080*Dv^2 + 2763408*Dv^4 + 21617280*Dv^6 + 152005248*Dv^8 + 671846400*Dv^10 - ... 2543040*Ev^2 + 36638048*Dv^2*Ev^2 - 230191488*Dv^4*Ev^2 - 568705536*Dv^6*Ev^2 - ... 3359232000*Dv^8*Ev^2 + 62857488*Ev^4 - 1045390464*Dv^2*Ev^4 + 5017261824*Dv^4*Ev^4 + ... 6718464000*Dv^6*Ev^4 - 580756608*Ev^6 + 7402876416*Dv^2*Ev^6 - 6718464000*Dv^4*Ev^6 + ... 1755976320*Ev^8 + 3359232000*Dv^2*Ev^8 - 671846400*Ev^10); coef(7)=-4*(2981 - 47320*Dv^2 - 64120*Dv^4 + 9673216*Dv^6 - 39392640*Dv^8 + 183472128*Dv^10 + 298598400*Dv^12 - ... 386040*Ev^2 + 9952752*Dv^2*Ev^2 - 34400256*Dv^4*Ev^2 - 850106880*Dv^6*Ev^2 + ... 2879483904*Dv^8*Ev^2 - 1791590400*Dv^10*Ev^2 + 15128712*Ev^4 - 442242560*Dv^2*Ev^4 + ... 1610972928*Dv^4*Ev^4 + 21290065920*Dv^6*Ev^4 + 4478976000*Dv^8*Ev^4 - 238902272*Ev^6 + ... 6435988992*Dv^2*Ev^6 + 434626560*Dv^4*Ev^6 - 5971968000*Dv^6*Ev^6 + 1549666944*Ev^8 - ... 22137090048*Dv^2*Ev^8 + 4478976000*Dv^4*Ev^8 - 2650558464*Ev^10 - 1791590400*Dv^2*Ev^10 + ... 298598400*Ev^12); coef(8)=4*(297 - 11192*Dv^2 + 237496*Dv^4 - 3876416*Dv^6 + 42056320*Dv^8 - 181665792*Dv^10 + 343719936*Dv^12 - ... 56184*Ev^2 + 2174160*Dv^2*Ev^2 - 23371584*Dv^4*Ev^2 + 190680576*Dv^6*Ev^2 - 2536390656*Dv^8*Ev^2 + ... 8427110400*Dv^10*Ev^2 + 3518712*Ev^4 - 133449408*Dv^2*Ev^4 + 637523712*Dv^4*Ev^4 + ... 511377408*Dv^6*Ev^4 + 34967863296*Dv^8*Ev^4 - 91362240*Ev^6 + 2910748160*Dv^2*Ev^6 + ... 5807702016*Dv^4*Ev^6 - 52144570368*Dv^6*Ev^6 + 1083122304*Ev^8 - 18530500608*Dv^2*Ev^8 - ... 32725057536*Dv^4*Ev^8 - 4945231872*Ev^10 + 37814501376*Dv^2*Ev^10 + 3316432896*Ev^12); coef(9)=-57 + 4320*Dv^2 - 156320*Dv^4 + 2990080*Dv^6 - 28816640*Dv^8 + 120471552*Dv^10 - 185794560*Dv^12 + ... 14688*Ev^2 - 962752*Dv^2*Ev^2 + 24949760*Dv^4*Ev^2 - 363031552*Dv^6*Ev^2 + 2756820992*Dv^8*Ev^2 - ... 6661472256*Dv^10*Ev^2 - 1350816*Ev^4 + 69888000*Dv^2*Ev^4 - 1203813888*Dv^4*Ev^4 + ... 11292278784*Dv^6*Ev^4 - 58655047680*Dv^8*Ev^4 + 56017920*Ev^6 - 1732537344*Dv^2*Ev^6 + ... 14348156928*Dv^4*Ev^6 - 813957120*Dv^6*Ev^6 - 1123202304*Ev^8 + 8542437376*Dv^2*Ev^8 - ... 126602772480*Dv^4*Ev^8 + 10503241728*Ev^10 + 35466117120*Dv^2*Ev^10 - 38236520448*Ev^12; coef(10)=(-1 + 56*Dv^2 - 784*Dv^4 + 2304*Dv^6 + 168*Ev^2 - 4704*Dv^2*Ev^2 + 46336*Dv^4*Ev^2 - 7056*Ev^4 + ... 11008*Dv^2*Ev^4 + 87808*Ev^6)^2; FLD22=roots(coef); FLD=sqrt([FLD21',FLD22'])*hv/tensor.g(3,3); case 7 clear coef; coef(1)=589824; coef(2)=-8192*(65 + 2880*Dv^2 - 2736*Ev^2); coef(3)=256*(713 + 24448*Dv^2 + 1216512*Dv^4 - 67488*Ev^2 - 1437696*Dv^2*Ev^2 + 1108224*Ev^4); coef(4)=-256*(115 - 1120*Dv^2 + 245760*Dv^4 + 5898240*Dv^6 - 18996*Ev^2 + 641664*Dv^2*Ev^2 - ... 31186944*Dv^4*Ev^2 + 785376*Ev^4 - 40209408*Dv^2*Ev^4 - 10810368*Ev^6); coef(5)=32*(71 - 4416*Dv^2 - 26624*Dv^4 + 8388608*Dv^6 + 75497472*Dv^8 - 18792*Ev^2 + 1737216*Dv^2*Ev^2 + ... 21676032*Dv^4*Ev^2 - 1538260992*Dv^6*Ev^2 + 1460592*Ev^4 - 150736896*Dv^2*Ev^4 - ... 1516142592*Dv^4*Ev^4 - 43953408*Ev^6 + 2845532160*Dv^2*Ev^6 + 430645248*Ev^8); coef(6)=16*(-5 + 800*Dv^2 - 51200*Dv^4 + 1966080*Dv^6 - 41943040*Dv^8 + 1932*Ev^2 - 277632*Dv^2*Ev^2 + ... 10862592*Dv^4*Ev^2 - 300417024*Dv^6*Ev^2 + 5435817984*Dv^8*Ev^2 - 246384*Ev^4 + ... 23864832*Dv^2*Ev^4 - 509607936*Dv^4*Ev^4 + 3906994176*Dv^6*Ev^4 + 13455936*Ev^6 - ... 560424960*Dv^2*Ev^6 + 14407041024*Dv^4*Ev^6 - 341065728*Ev^8 - 147308544*Dv^2*Ev^8 + ... 3392077824*Ev^10); coef(7)=-((-1 + 64*Dv^2 - 96*Dv*Ev + 96*Ev^2)*(-1 + 64*Dv^2 + 96*Dv*Ev + 96*Ev^2)*... (1 - 64*Dv^2 - 24*Ev + 768*Dv^2*Ev + 120*Ev^2 + 288*Ev^3 - 2160*Ev^4)*... (-1 + 64*Dv^2 - 24*Ev + 768*Dv^2*Ev - 120*Ev^2 + 288*Ev^3 + 2160*Ev^4)); FLD21=roots(coef); clear coef; coef(1)=-256; coef(2)=16*(9 + 128*Dv^2 - 720*Ev^2); coef(3)=-8*(3 - 48*Dv^2 + 512*Dv^4 - 540*Ev^2 + 9600*Dv^2*Ev^2 + 21600*Ev^4); coef(4)=(1 + 4*Dv - 60*Ev^2)*(-1 + 4*Dv + 60*Ev^2)*(-1 + 16*Dv^2 + 240*Ev^2); FLD22=roots(coef); clear coef; coef(1)=2025; coef(2)=-18*(367 - 870*Dv + 5175*Dv^2 - 5175*Ev^2); coef(3)=7711 - 38604*Dv + 144810*Dv^2 - 283500*Dv^3 + 1342575*Dv^4 - 267822*Ev^2 + 1151820*Dv*Ev^2 - ... 2685150*Dv^2*Ev^2 + 1342575*Ev^4; coef(4)=-4*(937 - 7774*Dv + 23727*Dv^2 - 39492*Dv^3 + 233847*Dv^4 - 572670*Dv^5 + 1897425*Dv^6 - 67011*Ev^2 + ... 532092*Dv*Ev^2 - 773154*Dv^2*Ev^2 - 1407780*Dv^3*Ev^2 - 5692275*Dv^4*Ev^2 + 978795*Ev^4 - ... 8387550*Dv*Ev^4 + 5692275*Dv^2*Ev^4 - 1897425*Ev^6); coef(5)=663 - 9048*Dv + 48356*Dv^2 - 59432*Dv^3 - 521430*Dv^4 + 1263384*Dv^5 + 4408740*Dv^6 - 10719000*Dv^7 + ... 15614775*Dv^8 - 105660*Ev^2 + 1199112*Dv*Ev^2 - 2752932*Dv^2*Ev^2 - 5934864*Dv^3*Ev^2 + ... 59348412*Dv^4*Ev^2 - 168748920*Dv^5*Ev^2 - 62459100*Dv^6*Ev^2 + 3460842*Ev^4 - 41473800*Dv*Ev^4 + ... 62868636*Dv^2*Ev^4 - 86537160*Dv^3*Ev^4 + 93688650*Dv^4*Ev^4 - 31848444*Ev^6 + 266005080*Dv*Ev^6 - ... 62459100*Dv^2*Ev^6 + 15614775*Ev^8; coef(6)=-2*(23 - 462*Dv + 2675*Dv^2 - 360*Dv^3 - 23042*Dv^4 - 4820*Dv^5 - 267634*Dv^6 + 1478424*Dv^7 + ... 2034603*Dv^8 - 7810830*Dv^9 + 6688575*Dv^10 - 6363*Ev^2 + 116664*Dv*Ev^2 - 525972*Dv^2*Ev^2 - ... 896184*Dv^3*Ev^2 + 9147390*Dv^4*Ev^2 - 7048056*Dv^5*Ev^2 + 14017068*Dv^6*Ev^2 - ... 152607240*Dv^7*Ev^2 - 33442875*Dv^8*Ev^2 + 473670*Ev^4 - 7237332*Dv*Ev^4 + 31480074*Dv^2*Ev^4 - ... 20626776*Dv^3*Ev^4 - 71012358*Dv^4*Ev^4 + 110702700*Dv^5*Ev^4 + 66885750*Dv^6*Ev^4 - ... 11516310*Ev^6 + 103020984*Dv*Ev^6 - 445531428*Dv^2*Ev^6 + 267659640*Dv^3*Ev^6 - ... 66885750*Dv^4*Ev^6 + 102360915*Ev^8 - 217944270*Dv*Ev^8 + 33442875*Dv^2*Ev^8 - 6688575*Ev^10); coef(7)=(-1 + 2*Dv + 15*Dv^2 + 6*Ev - 30*Dv*Ev + 15*Ev^2)*(-1 + 2*Dv + 15*Dv^2 - 6*Ev + 30*Dv*Ev + 15*Ev^2)*... (-1 + 12*Dv - 14*Dv^2 - 132*Dv^3 + 135*Dv^4 - 12*Ev + 156*Dv*Ev - 372*Dv^2*Ev - 540*Dv^3*Ev + ... 114*Ev^2 - 396*Dv*Ev^2 + 810*Dv^2*Ev^2 + 900*Ev^3 - 540*Dv*Ev^3 + 135*Ev^4)*... (-1 + 12*Dv - 14*Dv^2 - 132*Dv^3 + 135*Dv^4 + 12*Ev - 156*Dv*Ev + 372*Dv^2*Ev + 540*Dv^3*Ev + ... 114*Ev^2 - 396*Dv*Ev^2 + 810*Dv^2*Ev^2 - 900*Ev^3 + 540*Dv*Ev^3 + 135*Ev^4); FLD23=roots(coef); clear coef; coef(1)=2025; coef(2)=-18*(367 + 870*Dv + 5175*Dv^2 - 5175*Ev^2); coef(3)=7711 + 38604*Dv + 144810*Dv^2 + 283500*Dv^3 + 1342575*Dv^4 - 267822*Ev^2 - 1151820*Dv*Ev^2 - ... 2685150*Dv^2*Ev^2 + 1342575*Ev^4; coef(4)=-4*(937 + 7774*Dv + 23727*Dv^2 + 39492*Dv^3 + 233847*Dv^4 + 572670*Dv^5 + 1897425*Dv^6 - 67011*Ev^2 - ... 532092*Dv*Ev^2 - 773154*Dv^2*Ev^2 + 1407780*Dv^3*Ev^2 - 5692275*Dv^4*Ev^2 + 978795*Ev^4 + ... 8387550*Dv*Ev^4 + 5692275*Dv^2*Ev^4 - 1897425*Ev^6); coef(5)=663 + 9048*Dv + 48356*Dv^2 + 59432*Dv^3 - 521430*Dv^4 - 1263384*Dv^5 + 4408740*Dv^6 + 10719000*Dv^7 + ... 15614775*Dv^8 - 105660*Ev^2 - 1199112*Dv*Ev^2 - 2752932*Dv^2*Ev^2 + 5934864*Dv^3*Ev^2 + ... 59348412*Dv^4*Ev^2 + 168748920*Dv^5*Ev^2 - 62459100*Dv^6*Ev^2 + 3460842*Ev^4 + 41473800*Dv*Ev^4 + ... 62868636*Dv^2*Ev^4 + 86537160*Dv^3*Ev^4 + 93688650*Dv^4*Ev^4 - 31848444*Ev^6 - 266005080*Dv*Ev^6 - ... 62459100*Dv^2*Ev^6 + 15614775*Ev^8; coef(6)=-2*(23 + 462*Dv + 2675*Dv^2 + 360*Dv^3 - 23042*Dv^4 + 4820*Dv^5 - 267634*Dv^6 - 1478424*Dv^7 + ... 2034603*Dv^8 + 7810830*Dv^9 + 6688575*Dv^10 - 6363*Ev^2 - 116664*Dv*Ev^2 - 525972*Dv^2*Ev^2 + ... 896184*Dv^3*Ev^2 + 9147390*Dv^4*Ev^2 + 7048056*Dv^5*Ev^2 + 14017068*Dv^6*Ev^2 + ... 152607240*Dv^7*Ev^2 - 33442875*Dv^8*Ev^2 + 473670*Ev^4 + 7237332*Dv*Ev^4 + 31480074*Dv^2*Ev^4 + ... 20626776*Dv^3*Ev^4 - 71012358*Dv^4*Ev^4 - 110702700*Dv^5*Ev^4 + 66885750*Dv^6*Ev^4 - ... 11516310*Ev^6 - 103020984*Dv*Ev^6 - 445531428*Dv^2*Ev^6 - 267659640*Dv^3*Ev^6 - ... 66885750*Dv^4*Ev^6 + 102360915*Ev^8 + 217944270*Dv*Ev^8 + 33442875*Dv^2*Ev^8 - 6688575*Ev^10); coef(7)=(-1 - 2*Dv + 15*Dv^2 - 6*Ev - 30*Dv*Ev + 15*Ev^2)*(-1 - 2*Dv + 15*Dv^2 + 6*Ev + 30*Dv*Ev + 15*Ev^2)*... (-1 - 12*Dv - 14*Dv^2 + 132*Dv^3 + 135*Dv^4 + 12*Ev + 156*Dv*Ev + 372*Dv^2*Ev - 540*Dv^3*Ev + ... 114*Ev^2 + 396*Dv*Ev^2 + 810*Dv^2*Ev^2 - 900*Ev^3 - 540*Dv*Ev^3 + 135*Ev^4)*... (-1 - 12*Dv - 14*Dv^2 + 132*Dv^3 + 135*Dv^4 - 12*Ev - 156*Dv*Ev - 372*Dv^2*Ev + 540*Dv^3*Ev + ... 114*Ev^2 + 396*Dv*Ev^2 + 810*Dv^2*Ev^2 + 900*Ev^3 + 540*Dv*Ev^3 + 135*Ev^4); FLD24=roots(coef); FLD=sqrt([FLD21',FLD22',FLD23',FLD24'])*hv/tensor.g(3,3); case 8 clear coef; coef(1)=347892350976; coef(2)=-9663676416*(65 + 3312*Dv^2 - 5328*Ev^2); coef(3)=33554432*(14867 + 1137312*Dv^2 + 35686656*Dv^4 - 2554272*Ev^2 - 101564928*Dv^2*Ev^2 + 98972928*Ev^4); coef(4)=-4194304*(54625 + 4340592*Dv^2 + 235844352*Dv^4 + 5681000448*Dv^6 - 14841360*Ev^2 - ... 752491008*Dv^2*Ev^2 - 22993072128*Dv^4*Ev^2 + 1214906112*Ev^4 + 31612612608*Dv^2*Ev^4 - ... 29854199808*Ev^6); coef(5)=196608*(342555 + 21616704*Dv^2 + 1647872512*Dv^4 + 68918919168*Dv^6 + 1415236091904*Dv^8 - ... 131668800*Ev^2 - 4979663872*Dv^2*Ev^2 - 319332728832*Dv^4*Ev^2 - 7247382183936*Dv^6*Ev^2 + ... 17170272768*Ev^4 + 341494972416*Dv^2*Ev^4 + 15955728924672*Dv^4*Ev^4 - 900273291264*Ev^6 - ... 7570983223296*Dv^2*Ev^6 + 15996308226048*Ev^8); coef(6)=-131072*(101175 + 3110244*Dv^2 + 421060224*Dv^4 + 22531139584*Dv^6 + 824696193024*Dv^8 + ... 15109004722176*Dv^10 - 51910380*Ev^2 - 330579456*Dv^2*Ev^2 - 125948995584*Dv^4*Ev^2 - ... 4556852232192*Dv^6*Ev^2 - 93715901448192*Dv^8*Ev^2 + 9640065024*Ev^4 - 92408103936*Dv^2*Ev^4 + ... 14012157100032*Dv^4*Ev^4 + 228566166405120*Dv^6*Ev^4 - 812250934272*Ev^6 + ... 13651032342528*Dv^2*Ev^6 - 577160842051584*Dv^4*Ev^6 + 31126880600064*Ev^8 - ... 442580499431424*Dv^2*Ev^8 - 435856392585216*Ev^10); coef(7)=16384*(108795 - 1655592*Dv^2 + 370681968*Dv^4 + 20515171328*Dv^6 + 883183693824*Dv^8 + ... 32139341070336*Dv^10 + 528380448473088*Dv^12 - 71927640*Ev^2 + 2797159968*Dv^2*Ev^2 - ... 167917642752*Dv^4*Ev^2 - 6811593523200*Dv^6*Ev^2 - 177115857813504*Dv^8*Ev^2 - ... 3939399295303680*Dv^10*Ev^2 + 17931277296*Ev^4 - 972372722688*Dv^2*Ev^4 + 34027595513856*Dv^4*Ev^4 + ... 739804590637056*Dv^6*Ev^4 + 9095288535908352*Dv^8*Ev^4 - 2167633695744*Ev^6 + ... 132130580299776*Dv^2*Ev^6 - 3371794939772928*Dv^4*Ev^6 - 21069811798769664*Dv^6*Ev^6 + ... 134688166170624*Ev^8 - 7742449197121536*Dv^2*Ev^8 + 127900567842324480*Dv^4*Ev^8 - ... 4101716652982272*Ev^10 + 164202426736312320*Dv^2*Ev^10 + 48366040453742592*Ev^12); coef(8)=-24576*(6675 - 499332*Dv^2 + 30700368*Dv^4 + 557544768*Dv^6 + 34437854208*Dv^8 + 2071720214528*Dv^10 + ... 58586808188928*Dv^12 + 944862828429312*Dv^14 - 5547300*Ev^2 + 526937888*Dv^2*Ev^2 - ... 20335945792*Dv^4*Ev^2 - 475564220416*Dv^6*Ev^2 + 2143309053952*Dv^8*Ev^2 - ... 637929855123456*Dv^10*Ev^2 - 7313028689166336*Dv^12*Ev^2 + 1790304528*Ev^4 - ... 192817892160*Dv^2*Ev^4 + 5772679188480*Dv^4*Ev^4 + 156138306158592*Dv^6*Ev^4 - ... 3888913222729728*Dv^8*Ev^4 + 66904747268898816*Dv^10*Ev^4 - 292307161536*Ev^6 + ... 32929960734720*Dv^2*Ev^6 - 821736968601600*Dv^4*Ev^6 - 21036123288502272*Dv^6*Ev^6 + ... 429391466616324096*Dv^8*Ev^6 + 26246470265856*Ev^8 - 2853773353746432*Dv^2*Ev^8 + ... 55615868026748928*Dv^4*Ev^8 + 1019641052736258048*Dv^6*Ev^8 - 1304982933405696*Ev^10 + ... 121229370742800384*Dv^2*Ev^10 - 1342396465447698432*Dv^4*Ev^10 + 33544318563385344*Ev^12 - ... 1986915495076429824*Dv^2*Ev^12 - 348238364232646656*Ev^14); coef(9)=512*(19995 - 3025104*Dv^2 + 230260896*Dv^4 - 9286366464*Dv^6 + 559474127616*Dv^8 - ... 14678266527744*Dv^10 + 482863273607168*Dv^12 + 2216895952453632*Dv^14 + 75872635774304256*Dv^16 - ... 20467440*Ev^2 + 3319581120*Dv^2*Ev^2 - 188718494976*Dv^4*Ev^2 + 4378756285440*Dv^6*Ev^2 - ... 305571362193408*Dv^8*Ev^2 + 11713558579249152*Dv^10*Ev^2 - 218332196430151680*Dv^12*Ev^2 - ... 146727616093618176*Dv^14*Ev^2 + 8334140832*Ev^4 - 1392223811328*Dv^2*Ev^4 + ... 61369044632064*Dv^4*Ev^4 - 195442446532608*Dv^6*Ev^4 + 51857366512435200*Dv^8*Ev^4 - ... 2708385077900869632*Dv^10*Ev^4 + 27268157692050407424*Dv^12*Ev^4 - 1769809616640*Ev^6 + ... 292285012681728*Dv^2*Ev^6 - 9843621016928256*Dv^4*Ev^6 - 143847972363829248*Dv^6*Ev^6 - ... 3309885193338224640*Dv^8*Ev^6 + 192879935043831595008*Dv^10*Ev^6 + 215784762483456*Ev^8 - ... 33604060229517312*Dv^2*Ev^8 + 804738005551153152*Dv^4*Ev^8 + 20207497248679919616*Dv^6*Ev^8 + ... 111293410479578284032*Dv^8*Ev^8 - 15583830155476992*Ev^10 + 2133800464999514112*Dv^2*Ev^10 - ... 30913866387985268736*Dv^4*Ev^10 - 681701023552383221760*Dv^6*Ev^10 + 656086092564529152*Ev^12 - ... 69463071013371641856*Dv^2*Ev^12 + 424822111655442776064*Dv^4*Ev^12 - 14839387698656968704*Ev^14 + ... 886438028941977452544*Dv^2*Ev^14 + 139002809923368124416*Ev^16); coef(10)=-512*(825 - 204756*Dv^2 + 23245344*Dv^4 - 1575858816*Dv^6 + 70023154944*Dv^8 - 1101156566016*Dv^10 - ... 20419794927616*Dv^12 + 1073192209219584*Dv^14 - 4745700631904256*Dv^16 + 79537657910132736*Dv^18 - ... 1021860*Ev^2 + 248733504*Dv^2*Ev^2 - 23115055488*Dv^4*Ev^2 + 1279535182848*Dv^6*Ev^2 - ... 56359246685184*Dv^8*Ev^2 + 841965680590848*Dv^10*Ev^2 + 22582213656182784*Dv^12*Ev^2 - ... 584030349214875648*Dv^14*Ev^2 + 1101014558400577536*Dv^16*Ev^2 + 514008864*Ev^4 - ... 119929286016*Dv^2*Ev^4 + 8886508475904*Dv^4*Ev^4 - 364046175111168*Dv^6*Ev^4 + ... 16428190204035072*Dv^8*Ev^4 - 223780148054065152*Dv^10*Ev^4 - 6102358241361002496*Dv^12*Ev^4 + ... 79514556281640714240*Dv^14*Ev^4 - 138154149504*Ev^6 + 30012307080192*Dv^2*Ev^6 - ... 1680504739817472*Dv^4*Ev^6 + 44722068958347264*Dv^6*Ev^6 - 2203962289188765696*Dv^8*Ev^6 + ... 23411319611540373504*Dv^10*Ev^6 + 481388291850145628160*Dv^12*Ev^6 + 21982090044672*Ev^8 - ... 4281912593593344*Dv^2*Ev^8 + 167217446808354816*Dv^4*Ev^8 - 2412267312012853248*Dv^6*Ev^8 + ... 142190622139584872448*Dv^8*Ev^8 - 816256485171161726976*Dv^10*Ev^8 - 2162000727585792*Ev^10 + ... 357632268176719872*Dv^2*Ev^10 - 8607927192152702976*Dv^4*Ev^10 + 50340456979450822656*Dv^6*Ev^10 - ... 3297964109177290752000*Dv^8*Ev^10 + 132445589620064256*Ev^12 - 17059537058035138560*Dv^2*Ev^12 + ... 206528591979765301248*Dv^4*Ev^12 - 120446921326039400448*Dv^6*Ev^12 - 4910847651879321600*Ev^14 + ... 421391006689954627584*Dv^2*Ev^14 - 1853000912900016046080*Dv^4*Ev^14 + 100671526327912759296*Ev^16 - ... 4041653823726982004736*Dv^2*Ev^16 - 872282810038125330432*Ev^18); coef(11)=192*(57 - 20904*Dv^2 + 3336368*Dv^4 - 296555264*Dv^6 + 15369692928*Dv^8 - 448734685184*Dv^10 + ... 9275590627328*Dv^12 - 225698856566784*Dv^14 + 4322568901754880*Dv^16 - 29559669714321408*Dv^18 + ... 135657697793015808*Dv^20 - 84120*Ev^2 + 28601504*Dv^2*Ev^2 - 3897433856*Dv^4*Ev^2 + ... 296377541632*Dv^6*Ev^2 - 13348811880448*Dv^8*Ev^2 + 304498696593408*Dv^10*Ev^2 - ... 4697515025498112*Dv^12*Ev^2 + 143622824647458816*Dv^14*Ev^2 - 2196003826484379648*Dv^16*Ev^2 + ... 5684499981583515648*Dv^18*Ev^2 + 51323952*Ev^4 - 15831320832*Dv^2*Ev^4 + 1791025076736*Dv^4*Ev^4 - ... 113117168898048*Dv^6*Ev^4 + 4334616449888256*Dv^8*Ev^4 - 69148598951215104*Dv^10*Ev^4 + ... 576881284387700736*Dv^12*Ev^4 - 27176755415557865472*Dv^14*Ev^4 + 276665359075783999488*Dv^16*Ev^4 - ... 17075066112*Ev^6 + 4634963444736*Dv^2*Ev^6 - 419543114969088*Dv^4*Ev^6 + ... 21456607161729024*Dv^6*Ev^6 - 683286609366614016*Dv^8*Ev^6 + 6205393537295450112*Dv^10*Ev^6 + ... 8598970679540318208*Dv^12*Ev^6 + 1512826586269225058304*Dv^14*Ev^6 + 3443638392576*Ev^8 - ... 789773593282560*Dv^2*Ev^8 + 55138119679291392*Dv^4*Ev^8 - 2246851552515194880*Dv^6*Ev^8 + ... 58622414812427059200*Dv^8*Ev^8 - 240628709355209883648*Dv^10*Ev^8 - ... 1837836285092667850752*Dv^12*Ev^8 - 442169794418688*Ev^10 + 81001407529820160*Dv^2*Ev^10 - ... 4201958023258963968*Dv^4*Ev^10 + 131535049127324811264*Dv^6*Ev^10 - ... 2679604116043006476288*Dv^8*Ev^10 + 2861132145806373027840*Dv^10*Ev^10 + 36847703815114752*Ev^12 - ... 4958591233630666752*Dv^2*Ev^12 + 184989345170960941056*Dv^4*Ev^12 - ... 3852258182897948688384*Dv^6*Ev^12 + 55557091179854246707200*Dv^8*Ev^12 - 1982743765077196800*Ev^14 + ... 171093125485616431104*Dv^2*Ev^14 - 4570719729464817745920*Dv^4*Ev^14 + ... 35509699762586816348160*Dv^6*Ev^14 + 66471789351840251904*Ev^16 - 2865855372415740149760*Dv^2*Ev^16 + ... 54465484899550538760192*Dv^4*Ev^16 - 1264920563763646562304*Ev^18 + ... 15101684222417965154304*Dv^2*Ev^18 + 10488406330048310673408*Ev^20); coef(12)=-32*(5 - 2532*Dv^2 + 538224*Dv^4 - 60803392*Dv^6 + 3786564864*Dv^8 - 116527598592*Dv^10 + ... 595903238144*Dv^12 + 68808400846848*Dv^14 - 2094828599771136*Dv^16 + 25448603889696768*Dv^18 - ... 131807043152510976*Dv^20 + 290863010178662400*Dv^22 - 8676*Ev^2 + 3902304*Dv^2*Ev^2 - ... 711615936*Dv^4*Ev^2 + 67819926528*Dv^6*Ev^2 - 3476955823104*Dv^8*Ev^2 + 80323126321152*Dv^10*Ev^2 + ... 221814550020096*Dv^12*Ev^2 - 54279889961877504*Dv^14*Ev^2 + 1192427775665897472*Dv^16*Ev^2 - ... 10270479882613948416*Dv^18*Ev^2 + 24311804519340048384*Dv^20*Ev^2 + 6320304*Ev^4 - ... 2465083584*Dv^2*Ev^4 + 377871220224*Dv^4*Ev^4 - 29250932299776*Dv^6*Ev^4 + ... 1151604440395776*Dv^8*Ev^4 - 16316971377868800*Dv^10*Ev^4 - 241656896330661888*Dv^12*Ev^4 + ... 12348671681139572736*Dv^14*Ev^4 - 185278915221211054080*Dv^16*Ev^4 + ... 1013668749467688370176*Dv^18*Ev^4 - 2553768000*Ev^6 + 836168832000*Dv^2*Ev^6 - ... 106194769680384*Dv^4*Ev^6 + 6423684454563840*Dv^6*Ev^6 - 176128557970636800*Dv^8*Ev^6 + ... 534904309042642944*Dv^10*Ev^6 + 49654189635472982016*Dv^12*Ev^6 - 881389245454683734016*Dv^14*Ev^6 + ... 5694218619719434371072*Dv^16*Ev^6 + 637612528896*Ev^8 - 168017106705408*Dv^2*Ev^8 + ... 17665620820733952*Dv^4*Ev^8 - 802157326678573056*Dv^6*Ev^8 + 13587700358759841792*Dv^8*Ev^8 + ... 152367961773705265152*Dv^10*Ev^8 - 3696590744402905792512*Dv^12*Ev^8 + ... 18637793539886684307456*Dv^14*Ev^8 - 103617958800384*Ev^10 + 20748874683801600*Dv^2*Ev^10 - ... 1827309224612118528*Dv^4*Ev^10 + 58188030824700444672*Dv^6*Ev^10 - 534656543765185953792*Dv^8*Ev^10 - ... 16242283219826258214912*Dv^10*Ev^10 + 93352292399471753428992*Dv^12*Ev^10 + 11229369750982656*Ev^12 - ... 1571144222260150272*Dv^2*Ev^12 + 119425232995331604480*Dv^4*Ev^12 - ... 2286659246604612009984*Dv^6*Ev^12 + 12678280381406795268096*Dv^8*Ev^12 + ... 496004266272312036163584*Dv^10*Ev^12 - 815875413474852864*Ev^14 + 69768493994943184896*Dv^2*Ev^14 - ... 4873375008570589839360*Dv^4*Ev^14 + 36349353320399065055232*Dv^6*Ev^14 - ... 249168572205253017993216*Dv^8*Ev^14 + 39183674291719372800*Ev^16 - 1602382832774947012608*Dv^2*Ev^16 + ... 115894613431204341350400*Dv^4*Ev^16 + 35406760727895122903040*Dv^6*Ev^16 - ... 1191820254729423814656*Ev^18 + 12216803564900497489920*Dv^2*Ev^18 - ... 1228896803820387069591552*Dv^4*Ev^18 + 20763061259914092478464*Ev^20 + ... 71096479110518311747584*Dv^2*Ev^20 - 157309580549474400337920*Ev^22); coef(13)=(1 - 336*Dv^2 + 39648*Dv^4 - 2038528*Dv^6 + 47851776*Dv^8 - 459841536*Dv^10 + 1194393600*Dv^12 - ... 1008*Ev^2 + 237888*Dv^2*Ev^2 - 21222144*Dv^4*Ev^2 + 797174784*Dv^6*Ev^2 - 12917366784*Dv^8*Ev^2 + ... 83416449024*Dv^10*Ev^2 + 356832*Ev^4 - 49289472*Dv^2*Ev^4 + 2806949376*Dv^4*Ev^4 - ... 65464713216*Dv^6*Ev^4 + 264438743040*Dv^8*Ev^4 - 57915648*Ev^6 + 4053224448*Dv^2*Ev^6 - ... 112117727232*Dv^4*Ev^6 + 2585049956352*Dv^6*Ev^6 + 4544854272*Ev^8 - 113998897152*Dv^2*Ev^8 - ... 1644679987200*Dv^4*Ev^8 - 165919186944*Ev^10 + 1390560804864*Dv^2*Ev^10 + 2212255825920*Ev^12)^2; FLD21=roots(coef); clear coef; coef(1)=45209390625; coef(2)=-65610000*(5303 + 110250*Dv^2 - 110250*Ev^2); coef(3)=145800*(8086979 + 273197700*Dv^2 + 3393495000*Dv^4 - 365822100*Ev^2 - 6786990000*Dv^2*Ev^2 + 3393495000*Ev^4); coef(4)=-1296*(1782961081 + 71147628450*Dv^2 + 1540688445000*Dv^4 + 14734912500000*Dv^6 - 133215865650*Ev^2 - ... 3586769910000*Dv^2*Ev^2 - 44204737500000*Dv^4*Ev^2 + 2739363705000*Ev^4 + 44204737500000*Dv^2*Ev^4 - ... 14734912500000*Ev^6); coef(5)=36*(80362212791 + 3248632697832*Dv^2 + 92298474378000*Dv^4 + 1579080426480000*Dv^6 + ... 12856345110000000*Dv^8 - 8942562239688*Ev^2 - 240238005040800*Dv^2*Ev^2 - ... 5299968393360000*Dv^4*Ev^2 - 51425380440000000*Dv^6*Ev^2 + 308623833018000*Ev^4 + ... 5689704390480000*Dv^2*Ev^4 + 77138070660000000*Dv^4*Ev^4 - 3804905450160000*Ev^6 - ... 51425380440000000*Dv^2*Ev^6 + 12856345110000000*Ev^8); coef(6)=-16*(150970020559 + 5586969331746*Dv^2 + 184777411658832*Dv^4 + 4297018993848000*Dv^6 + ... 63526835785680000*Dv^8 + 463522840200000000*Dv^10 - 23848340096322*Ev^2 - 486175053786336*Dv^2*Ev^2 - ... 15908813810856000*Dv^4*Ev^2 - 275434458359040000*Dv^6*Ev^2 - 2317614201000000000*Dv^8*Ev^2 + ... 1242083822568336*Ev^4 + 13314119415451200*Dv^2*Ev^4 + 476405657632800000*Dv^4*Ev^4 + ... 4635228402000000000*Dv^6*Ev^4 - 26378586551160000*Ev^6 - 196806573555840000*Dv^2*Ev^6 - ... 4635228402000000000*Dv^4*Ev^6 + 217283207337360000*Ev^8 + 2317614201000000000*Dv^2*Ev^8 - ... 463522840200000000*Ev^10); coef(7)=8*(170848612093 + 5387879558004*Dv^2 + 186901958240280*Dv^4 + 5624941117958784*Dv^6 + ... 110538527809392000*Dv^8 + 1496870793682560000*Dv^10 + 10073201977440000000*Dv^12 - ... 37443475278468*Ev^2 - 362559302014896*Dv^2*Ev^2 - 21609987219333504*Dv^4*Ev^2 - ... 540854356447756800*Dv^6*Ev^2 - 7845030156493440000*Dv^8*Ev^2 - 60439211864640000000*Dv^10*Ev^2 + ... 2797421509490328*Ev^4 - 9706482614007936*Dv^2*Ev^4 + 1101706798821408000*Dv^4*Ev^4 + ... 17592402430920960000*Dv^6*Ev^4 + 151098029661600000000*Dv^8*Ev^4 - 91474237990813824*Ev^6 + ... 861169247252928000*Dv^2*Ev^6 - 25558010368277760000*Dv^4*Ev^6 - 201464039548800000000*Dv^6*Ev^6 + ... 1352003249849328000*Ev^8 - 9155201659056000000*Dv^2*Ev^8 + 151098029661600000000*Dv^4*Ev^8 - ... 7876696679176320000*Ev^10 - 60439211864640000000*Dv^2*Ev^10 + 10073201977440000000*Ev^12); coef(8)=-16*(32838674665 + 826858406490*Dv^2 + 26359199605944*Dv^4 + 1120619663719776*Dv^6 + ... 24679124048126592*Dv^8 + 473062168230336000*Dv^10 + 5908865329831680000*Dv^12 + ... 37470700310400000000*Dv^14 - 9865232636490*Ev^2 + 32035753237872*Dv^2*Ev^2 - ... 3752526821472288*Dv^4*Ev^2 - 164189437874039808*Dv^6*Ev^2 - 2291991960075148800*Dv^8*Ev^2 - ... 37936114597670400000*Dv^10*Ev^2 - 262294902172800000000*Dv^12*Ev^2 + 1030859185891032*Ev^4 - ... 21721695325256160*Dv^2*Ev^4 + 375495114504658176*Dv^4*Ev^4 + 9149286835100851200*Dv^6*Ev^4 + ... 72255789173986560000*Dv^8*Ev^4 + 786884706518400000000*Dv^10*Ev^4 - 49093314672384864*Ev^6 + ... 1523719063713226752*Dv^2*Ev^6 - 19311963512595840000*Dv^4*Ev^6 - 216559418841953280000*Dv^6*Ev^6 - ... 1311474510864000000000*Dv^8*Ev^6 + 1148581815080897664*Ev^8 - 37920250285351948800*Dv^2*Ev^8 + ... 329990186024720640000*Dv^4*Ev^8 + 1311474510864000000000*Dv^6*Ev^8 - 12735219775692326400*Ev^10 + ... 293741427727434240000*Dv^2*Ev^10 - 786884706518400000000*Dv^4*Ev^10 + 54129915398050560000*Ev^12 + ... 262294902172800000000*Dv^2*Ev^12 - 37470700310400000000*Ev^14); coef(9)=2*(68590746195 + 1081602708240*Dv^2 + 48335475577632*Dv^4 + 1340669358336256*Dv^6 + ... 71195882290156800*Dv^8 + 987743387378036736*Dv^10 + 22196744950311936000*Dv^12 + ... 250254659764592640000*Dv^14 + 1522404832596480000000*Dv^16 - 27874279273680*Ev^2 + ... 494651329980096*Dv^2*Ev^2 - 6579257352367872*Dv^4*Ev^2 - 473322991393760256*Dv^6*Ev^2 - ... 6884892594788216832*Dv^8*Ev^2 - 113156341929968025600*Dv^10*Ev^2 - ... 1927974701161635840000*Dv^12*Ev^2 - 12179238660771840000000*Dv^14*Ev^2 + 4019222549991456*Ev^4 - ... 161121343320329472*Dv^2*Ev^4 + 1617172195984657920*Dv^4*Ev^4 + 60996138700807987200*Dv^6*Ev^4 - ... 117606766589512704000*Dv^8*Ev^4 + 6556002555206246400000*Dv^10*Ev^4 + ... 42627335312701440000000*Dv^12*Ev^4 - 270732524551826688*Ev^6 + 14507242576033987584*Dv^2*Ev^6 - ... 159647787630854037504*Dv^4*Ev^6 - 3366912287814502809600*Dv^6*Ev^6 + ... 19810818465057054720000*Dv^8*Ev^6 - 85254670625402880000000*Dv^10*Ev^6 + 9400869564077327616*Ev^8 - ... 557442793864140263424*Dv^2*Ev^8 + 5243873418176173056000*Dv^4*Ev^8 + ... 77836980573065502720000*Dv^6*Ev^8 + 106568338281753600000000*Dv^8*Ev^8 - 170702150869421715456*Ev^10 + ... 9371719157876103168000*Dv^2*Ev^10 - 45206272850010808320000*Dv^4*Ev^10 - ... 85254670625402880000000*Dv^6*Ev^10 + 1492212930919212441600*Ev^12 - ... 52717847384487075840000*Dv^2*Ev^12 + 42627335312701440000000*Dv^4*Ev^12 - ... 4601961317433876480000*Ev^14 - 12179238660771840000000*Dv^2*Ev^14 + 1522404832596480000000*Ev^16); coef(10)=-16*(1529961405 - 7475738370*Dv^2 + 2890609488480*Dv^4 - 102797616375680*Dv^6 + 4919803125475584*Dv^8 - ... 28883219712666624*Dv^10 + 990112035878019072*Dv^12 + 8456142408118272000*Dv^14 + ... 113847159433236480000*Dv^16 + 647381113344000000000*Dv^18 - 820765883070*Ev^2 + ... 30332388596160*Dv^2*Ev^2 - 632577217708416*Dv^4*Ev^2 + 13661058516443136*Dv^6*Ev^2 - ... 1165340410083025920*Dv^8*Ev^2 + 16287898705777704960*Dv^10*Ev^2 - 234571859878308249600*Dv^12*Ev^2 - ... 526279602782453760000*Dv^14*Ev^2 - 5826430020096000000000*Dv^16*Ev^2 + 161079531252192*Ev^4 - ... 9812006743630464*Dv^2*Ev^4 + 137251124615858688*Dv^4*Ev^4 + 1505140887807903744*Dv^6*Ev^4 + ... 63225393417181421568*Dv^8*Ev^4 - 1854680853772328140800*Dv^10*Ev^4 + ... 17380283964853616640000*Dv^12*Ev^4 + 23305720080384000000000*Dv^14*Ev^4 - 15091996816356480*Ev^6 + ... 1143704177908623360*Dv^2*Ev^6 - 15601953527436625920*Dv^4*Ev^6 - 321663866581783904256*Dv^6*Ev^6 + ... 594307955863675699200*Dv^8*Ev^6 + 76977010597776998400000*Dv^10*Ev^6 - ... 54380013520896000000000*Dv^12*Ev^6 + 750637488648455424*Ev^8 - 61848019073580014592*Dv^2*Ev^8 + ... 701627176080994590720*Dv^4*Ev^8 + 18030224490543717580800*Dv^6*Ev^8 + ... 8828994138450370560000*Dv^8*Ev^8 + 81570020281344000000000*Dv^10*Ev^8 - 20648683447588869120*Ev^10 + ... 1640773044782641889280*Dv^2*Ev^10 - 10072933109553151180800*Dv^4*Ev^10 - ... 227861633269311160320000*Dv^6*Ev^10 - 81570020281344000000000*Dv^8*Ev^10 + ... 307331748996352155648*Ev^12 - 19594407395023722086400*Dv^2*Ev^12 + ... 41323202506199531520000*Dv^4*Ev^12 + 54380013520896000000000*Dv^6*Ev^12 - ... 2166120690388424294400*Ev^14 + 79228941407737528320000*Dv^2*Ev^14 - ... 23305720080384000000000*Dv^4*Ev^14 + 4535633097642332160000*Ev^16 + ... 5826430020096000000000*Dv^2*Ev^16 - 647381113344000000000*Ev^18); coef(11)=8*(375557685 - 16273971060*Dv^2 + 1745695700040*Dv^4 - 58921592510720*Dv^6 + 174872453184768*Dv^8 + ... 68196563498870784*Dv^10 - 1467933721645731840*Dv^12 + 19401184966088392704*Dv^14 - ... 22314213657169920000*Dv^16 + 627934813833461760000*Dv^18 + 2819109202624512000000*Dv^20 - ... 258630620220*Ev^2 + 17917449118320*Dv^2*Ev^2 - 839115396645120*Dv^4*Ev^2 + ... 34137657663771648*Dv^6*Ev^2 - 857878588532287488*Dv^8*Ev^2 - 3330417550681055232*Dv^10*Ev^2 + ... 367486332062767054848*Dv^12*Ev^2 - 5104018622648549376000*Dv^14*Ev^2 + ... 8858155467780587520000*Dv^16*Ev^2 - 28191092026245120000000*Dv^18*Ev^2 + 67341924318024*Ev^4 - ... 5944521399945984*Dv^2*Ev^4 + 178472070403204608*Dv^4*Ev^4 - 4100686062655500288*Dv^6*Ev^4 + ... 152999045473146163200*Dv^8*Ev^4 - 1484444743673177899008*Dv^10*Ev^4 - ... 28617601482849927168000*Dv^12*Ev^4 + 356864018486380462080000*Dv^14*Ev^4 + ... 126859914118103040000000*Dv^16*Ev^4 - 8633530620820224*Ev^6 + 862827688268448768*Dv^2*Ev^6 - ... 19959049015677702144*Dv^4*Ev^6 + 60365036905400254464*Dv^6*Ev^6 - 8870920966190951497728*Dv^8*Ev^6 + ... 140547181723769910067200*Dv^10*Ev^6 + 1139150299196255109120000*Dv^12*Ev^6 - ... 338293104314941440000000*Dv^14*Ev^6 + 601864247308633344*Ev^8 - 62136081840535713792*Dv^2*Ev^8 + ... 1039353862772405293056*Dv^4*Ev^8 + 13901425503084450349056*Dv^6*Ev^8 + ... 296588419017751122739200*Dv^8*Ev^8 - 2149721369479055278080000*Dv^10*Ev^8 + ... 592012932551147520000000*Dv^12*Ev^8 - 23998402745009031168*Ev^10 + 2326515770772462624768*Dv^2*Ev^10 - ... 19798234526476362645504*Dv^4*Ev^10 - 481742274128571688550400*Dv^6*Ev^10 - ... 2877261369741443727360000*Dv^8*Ev^10 - 710415519061377024000000*Dv^10*Ev^10 + ... 552442068067375263744*Ev^12 - 43599195944215061004288*Dv^2*Ev^12 + ... 100974265562215032422400*Dv^4*Ev^12 + 4630936406633596846080000*Dv^6*Ev^12 + ... 592012932551147520000000*Dv^8*Ev^12 - 6956111575735113940992*Ev^14 + ... 365842058775408318873600*Dv^2*Ev^14 + 15939810784747192320000*Dv^4*Ev^14 - ... 338293104314941440000000*Dv^6*Ev^14 + 39816513383981985792000*Ev^16 - ... 1076503096758173368320000*Dv^2*Ev^16 + 126859914118103040000000*Dv^4*Ev^16 - ... 48890789403921285120000*Ev^18 - 28191092026245120000000*Dv^2*Ev^18 + 2819109202624512000000*Ev^20); coef(12)=-16*(15846915 - 1618195290*Dv^2 + 153642619320*Dv^4 - 5592487072800*Dv^6 + 76036092053760*Dv^8 - ... 2051123498234880*Dv^10 + 179109954117013504*Dv^12 - 4568604056221630464*Dv^14 + ... 53729515704561795072*Dv^16 - 191050717816258560000*Dv^18 + 739155476702822400000*Dv^20 + ... 1774861245480960000000*Dv^22 - 13656132630*Ev^2 + 1632327929328*Dv^2*Ev^2 - ... 112028819420064*Dv^4*Ev^2 + 4365067420022784*Dv^6*Ev^2 - 63682345860701184*Dv^8*Ev^2 - ... 680221785237430272*Dv^10*Ev^2 - 1411377735297908736*Dv^12*Ev^2 + 902729146121612034048*Dv^14*Ev^2 - ... 13370637139832792678400*Dv^16*Ev^2 + 36122872390672711680000*Dv^18*Ev^2 - ... 19523473700290560000000*Dv^20*Ev^2 + 4582687453272*Ev^4 - 594851088506976*Dv^2*Ev^4 + ... 31807752423510528*Dv^4*Ev^4 - 1057947280488105984*Dv^6*Ev^4 + 21117951997120622592*Dv^8*Ev^4 + ... 55094327640845402112*Dv^10*Ev^4 - 4918414035221313748992*Dv^12*Ev^4 - ... 49752093676841651404800*Dv^14*Ev^4 + 861531105280815267840000*Dv^16*Ev^4 + ... 97617368501452800000000*Dv^18*Ev^4 - 782155956697056*Ev^6 + 103554306218151936*Dv^2*Ev^6 - ... 4286992769017362432*Dv^4*Ev^6 + 95824702284683231232*Dv^6*Ev^6 - 2333532461165567852544*Dv^8*Ev^6 + ... 2694963190177856618496*Dv^10*Ev^6 + 455376442026839585587200*Dv^12*Ev^6 + ... 1637653228112691855360000*Dv^14*Ev^6 - 292852105504358400000000*Dv^16*Ev^6 + 74849235896671488*Ev^8 - ... 9496864430861976576*Dv^2*Ev^8 + 279461764678610644992*Dv^4*Ev^8 - 3083671428147661455360*Dv^6*Ev^8 + ... 118930125156640494649344*Dv^8*Ev^8 - 103547060748734496768000*Dv^10*Ev^8 - ... 8333675733613569638400000*Dv^12*Ev^8 + 585704211008716800000000*Dv^14*Ev^8 - ... 4205258104777436160*Ev^10 + 470948894751026700288*Dv^2*Ev^10 - 7859121855745069891584*Dv^4*Ev^10 + ... 35539680335008953139200*Dv^6*Ev^10 - 2300815812776791257907200*Dv^8*Ev^10 + ... 808370953757204152320000*Dv^10*Ev^10 - 819985895412203520000000*Dv^12*Ev^10 + ... 141698865927297650688*Ev^12 - 12269128627366694240256*Dv^2*Ev^12 + ... 80051068388331850825728*Dv^4*Ev^12 + 407607464357510381568000*Dv^6*Ev^12 + ... 15194084503164231352320000*Dv^8*Ev^12 + 819985895412203520000000*Dv^10*Ev^12 - ... 2820549745834769793024*Ev^14 + 154894522998248347926528*Dv^2*Ev^14 - ... 109280246462363389132800*Dv^4*Ev^14 - 10873157695648290570240000*Dv^6*Ev^14 - ... 585704211008716800000000*Dv^8*Ev^14 + 30677839898222896054272*Ev^16 - ... 842961865900766625792000*Dv^2*Ev^16 - 1470881606154214440960000*Dv^4*Ev^16 + ... 292852105504358400000000*Dv^6*Ev^16 - 145570849229390118912000*Ev^18 + ... 2056779074173324492800000*Dv^2*Ev^18 - 97617368501452800000000*Dv^4*Ev^18 + ... 82434143060431994880000*Ev^20 + 19523473700290560000000*Dv^2*Ev^20 - 1774861245480960000000*Ev^22); coef(13)=4*(3636735 - 657674760*Dv^2 + 69110591280*Dv^4 - 3304604983680*Dv^6 + 86566788147840*Dv^8 - ... 1570941543567360*Dv^10 - 284076821684224*Dv^12 + 1715201532159787008*Dv^14 - ... 49181736923644723200*Dv^16 + 568212015953627578368*Dv^18 - 2367084128978652364800*Dv^20 + ... 5289496404484423680000*Dv^22 + 3932000297680896000000*Dv^24 - 3838325400*Ev^2 + ... 719677964832*Dv^2*Ev^2 - 63659898252672*Dv^4*Ev^2 + 2758747259487744*Dv^6*Ev^2 - ... 53686166730387456*Dv^8*Ev^2 + 496413533420175360*Dv^10*Ev^2 - 11534442655208767488*Dv^12*Ev^2 + ... 44986240958303305728*Dv^14*Ev^2 + 8452748626223875227648*Dv^16*Ev^2 - ... 132568008144974983987200*Dv^18*Ev^2 + 398924790382901329920000*Dv^20*Ev^2 - ... 47184003572170752000000*Dv^22*Ev^2 + 1616800836528*Ev^4 - 302214540304512*Dv^2*Ev^4 + ... 22766289846292224*Dv^4*Ev^4 - 847343778516246528*Dv^6*Ev^4 + 13797134654876983296*Dv^8*Ev^4 + ... 10769121427776012288*Dv^10*Ev^4 + 186568866081975435264*Dv^12*Ev^4 - ... 55109464556948642856960*Dv^14*Ev^4 - 302820759611630419968000*Dv^16*Ev^4 + ... 7900455409459553894400000*Dv^18*Ev^4 + 259512019646939136000000*Dv^20*Ev^4 - 356466977788032*Ev^6 + ... 63448695695992320*Dv^2*Ev^6 - 3954193472683597824*Dv^4*Ev^6 + 120557867211286806528*Dv^6*Ev^6 - ... 1829814614778235650048*Dv^8*Ev^6 - 6858303038588345647104*Dv^10*Ev^6 + ... 136856516639863729029120*Dv^12*Ev^6 + 4949564247782719488000000*Dv^14*Ev^6 + ... 5247932407253575925760000*Dv^16*Ev^6 - 865040065489797120000000*Dv^18*Ev^6 + 45455946277935744*Ev^8 - ... 7268294418332848128*Dv^2*Ev^8 + 349354630879735947264*Dv^4*Ev^8 - 8565313342657449885696*Dv^6*Ev^8 + ... 126029471081710044119040*Dv^8*Ev^8 + 394734123545376432586752*Dv^10*Ev^8 - ... 6762732832605335873126400*Dv^12*Ev^8 - 92686485701301192622080000*Dv^14*Ev^8 + ... 1946340147352043520000000*Dv^16*Ev^8 - 3506160314559393792*Ev^10 + 462831362878600691712*Dv^2*Ev^10 - ... 15421396283541403140096*Dv^4*Ev^10 + 327848434757964618006528*Dv^6*Ev^10 - ... 3770944681237652994785280*Dv^8*Ev^10 - 10901997584346401420083200*Dv^10*Ev^10 + ... 99178637606137437880320000*Dv^12*Ev^10 - 3114144235763269632000000*Dv^14*Ev^10 + ... 166778996055241089024*Ev^12 - 15891420781750207315968*Dv^2*Ev^12 + ... 335567842948035981213696*Dv^4*Ev^12 - 5468347472652046511898624*Dv^6*Ev^12 + ... 56088822066311281508352000*Dv^8*Ev^12 + 106937390293062569164800000*Dv^10*Ev^12 + ... 3633168275057147904000000*Dv^12*Ev^12 - 4893722367578707525632*Ev^14 + ... 266169454588719265480704*Dv^2*Ev^14 - 3823530631362621430824960*Dv^4*Ev^14 + ... 15458060618562808892620800*Dv^6*Ev^14 - 226671905905375916851200000*Dv^8*Ev^14 - ... 3114144235763269632000000*Dv^10*Ev^14 + 85696882578256575430656*Ev^16 - ... 1704639720925306429636608*Dv^2*Ev^16 + 20996674678088278002892800*Dv^4*Ev^16 + ... 91501757160180091453440000*Dv^6*Ev^16 + 1946340147352043520000000*Dv^8*Ev^16 - ... 817664931625052805267456*Ev^18 + 1447303939377914393395200*Dv^2*Ev^18 + ... 25287856643231742689280000*Dv^4*Ev^18 - 865040065489797120000000*Dv^6*Ev^18 + ... 3304941211388670168268800*Ev^20 - 16481728645972151500800000*Dv^2*Ev^20 + ... 259512019646939136000000*Dv^4*Ev^20 - 618123553463095787520000*Ev^22 - ... 47184003572170752000000*Dv^2*Ev^22 + 3932000297680896000000*Ev^24); coef(14)=-16*(34509 - 9609450*Dv^2 + 1257447504*Dv^4 - 83668288320*Dv^6 + 3160972366464*Dv^8 - ... 58640419530240*Dv^10 - 330555594039296*Dv^12 + 36655008810762240*Dv^14 - 405377866120200192*Dv^16 - ... 4518107412813840384*Dv^18 + 110389841562483818496*Dv^20 - 568950040957236019200*Dv^22 + ... 1151603533896744960000*Dv^24 - 43808310*Ev^2 + 11840084256*Dv^2*Ev^2 - 1337534872128*Dv^4*Ev^2 + ... 73629528115200*Dv^6*Ev^2 - 2012135049429504*Dv^8*Ev^2 + 19007077725683712*Dv^10*Ev^2 + ... 531379933092347904*Dv^12*Ev^2 - 24783263937228570624*Dv^14*Ev^2 + 383512988914115936256*Dv^16*Ev^2 - ... 764521687015294500864*Dv^18*Ev^2 - 25256287237959371980800*Dv^20*Ev^2 + ... 98701945250229780480000*Dv^22*Ev^2 + 22650525072*Ev^4 - 5786479820736*Dv^2*Ev^4 + ... 559344945404160*Dv^4*Ev^4 - 24869792036846592*Dv^6*Ev^4 + 446572162806276096*Dv^8*Ev^4 + ... 2508382629352931328*Dv^10*Ev^4 - 223268407804353576960*Dv^12*Ev^4 + ... 4612468028132526391296*Dv^14*Ev^4 - 61436604679513045991424*Dv^16*Ev^4 + ... 172839320279342854963200*Dv^18*Ev^4 + 1745480732961857863680000*Dv^20*Ev^4 - 6277790630592*Ev^6 + ... 1461424845597696*Dv^2*Ev^6 - 118228796689351680*Dv^4*Ev^6 + 4291876071000539136*Dv^6*Ev^6 - ... 52970608520389361664*Dv^8*Ev^6 - 926632314423388274688*Dv^10*Ev^6 + ... 27067588000011644829696*Dv^12*Ev^6 - 243302262168255863980032*Dv^14*Ev^6 + ... 2269548904906900478361600*Dv^16*Ev^6 - 983729768080909271040000*Dv^18*Ev^6 + 1034124875358336*Ev^8 - ... 208223228887285248*Dv^2*Ev^8 + 13712265223603347456*Dv^4*Ev^8 - 423105643429052645376*Dv^6*Ev^8 + ... 4492436516397132742656*Dv^8*Ev^8 + 68282260811949858619392*Dv^10*Ev^8 - ... 1172152561994163095076864*Dv^12*Ev^8 + 5505269591073077644492800*Dv^14*Ev^8 - ... 21875594316821173370880000*Dv^16*Ev^8 - 106087243771353600*Ev^10 + 17055096191539789824*Dv^2*Ev^10 - ... 888917217630124474368*Dv^4*Ev^10 + 23153571029440476610560*Dv^6*Ev^10 - ... 208391354835407133474816*Dv^8*Ev^10 - 3058520315071971427614720*Dv^10*Ev^10 + ... 11966649622348830238310400*Dv^12*Ev^10 + 45539868943208058716160000*Dv^14*Ev^10 + ... 6908884244595449856*Ev^12 - 776704274305434353664*Dv^2*Ev^12 + 32373685547750612533248*Dv^4*Ev^12 - ... 575348030325148728950784*Dv^6*Ev^12 + 6058059537304107110891520*Dv^8*Ev^12 + ... 63999898008193701878169600*Dv^10*Ev^12 - 3976162813133161758720000*Dv^12*Ev^12 - ... 285913255705042452480*Ev^14 + 17624351532781122748416*Dv^2*Ev^14 - ... 710821999771330066513920*Dv^4*Ev^14 + 3681715189466312359280640*Dv^6*Ev^14 - ... 64591821006479171990323200*Dv^8*Ev^14 - 69870551819230547804160000*Dv^10*Ev^14 + ... 7388726648989923901440*Ev^16 - 138324460812785222418432*Dv^2*Ev^16 + ... 9187918884941469239476224*Dv^4*Ev^16 + 20384509539719385081446400*Dv^6*Ev^16 + ... 70648701632699946762240000*Dv^8*Ev^16 - 113594227631625528410112*Ev^18 - ... 774961411167100738732032*Dv^2*Ev^18 - 47410795522372139797708800*Dv^4*Ev^18 - ... 16591724526499182673920000*Dv^6*Ev^18 + 925762715666719237472256*Ev^20 + ... 10531708725339313982668800*Dv^2*Ev^20 - 8226656918146299985920000*Dv^4*Ev^20 - ... 2801981945730323762380800*Ev^22 + 3368308735005362749440000*Dv^2*Ev^22 + 122206569251922247680000*Ev^24); coef(15)=8*(1643 - 649284*Dv^2 + 113185608*Dv^4 - 11241380224*Dv^6 + 743939411328*Dv^8 - 35534050397184*Dv^10 + ... 1276908244563968*Dv^12 - 34789066721132544*Dv^14 + 686137046696165376*Dv^16 - ... 8884585322053632000*Dv^18 + 66737806516408025088*Dv^20 - 244000382493759897600*Dv^22 + ... 352007645697146880000*Dv^24 - 2468844*Ev^2 + 901508592*Dv^2*Ev^2 - 134760736128*Dv^4*Ev^2 + ... 11253690600960*Dv^6*Ev^2 - 636332590568448*Dv^8*Ev^2 + 27001610560942080*Dv^10*Ev^2 - ... 861688244292747264*Dv^12*Ev^2 + 19814554952658321408*Dv^14*Ev^2 - 317300292533418983424*Dv^16*Ev^2 + ... 3356242221330887344128*Dv^18*Ev^2 - 19834694937727796772864*Dv^20*Ev^2 + ... 42193612221119358566400*Dv^22*Ev^2 + 1537103304*Ev^4 - 507030148224*Dv^2*Ev^4 + ... 63498546720000*Dv^4*Ev^4 - 4276955480242176*Dv^6*Ev^4 + 193942468356507648*Dv^8*Ev^4 - ... 6937160120067096576*Dv^10*Ev^4 + 194813531616280707072*Dv^12*Ev^4 - ... 3766419335092679737344*Dv^14*Ev^4 + 45989112762273210826752*Dv^16*Ev^4 - ... 349330735598906665598976*Dv^18*Ev^4 + 1319511394880694779904000*Dv^20*Ev^4 - 523161410688*Ev^6 + ... 150985404532224*Dv^2*Ev^6 - 15469639887218688*Dv^4*Ev^6 + 809009936488636416*Dv^6*Ev^6 - ... 26526243055336095744*Dv^8*Ev^6 + 699889102167163797504*Dv^10*Ev^6 - ... 16234079461009243766784*Dv^12*Ev^6 + 245388062656491643994112*Dv^14*Ev^6 - ... 1828007674356637359931392*Dv^16*Ev^6 + 4965202183226930705203200*Dv^18*Ev^6 + 108245460578688*Ev^8 - ... 26149013067267072*Dv^2*Ev^8 + 2164397814865299456*Dv^4*Ev^8 - 85705171035787689984*Dv^6*Ev^8 + ... 1777368789329363140608*Dv^8*Ev^8 - 25988317128437403746304*Dv^10*Ev^8 + ... 521517761451329253801984*Dv^12*Ev^8 - 6659545016817266171314176*Dv^14*Ev^8 + ... 43260067152658626615705600*Dv^16*Ev^8 - 14306421811627008*Ev^10 + 2712694125058928640*Dv^2*Ev^10 - ... 181626779168232505344*Dv^4*Ev^10 + 5229138820379712159744*Dv^6*Ev^10 - ... 57730851986536362147840*Dv^8*Ev^10 + 5877314375460115709952*Dv^10*Ev^10 - ... 7764573568064089774620672*Dv^12*Ev^10 + 2688281605572271276032000*Dv^14*Ev^10 + ... 1233772317919475712*Ev^12 - 165960317170346950656*Dv^2*Ev^12 + 9267425846766320615424*Dv^4*Ev^12 - ... 167131358441241493635072*Dv^6*Ev^12 + 853432472549896753250304*Dv^8*Ev^12 + ... 24119037096082648319655936*Dv^10*Ev^12 + 177881303838037516694323200*Dv^12*Ev^12 - ... 69582396190537875456*Ev^14 + 5579876788106538516480*Dv^2*Ev^14 - 289156718148572298608640*Dv^4*Ev^14 + ... 1829965856255044975853568*Dv^6*Ev^14 - 5150387598132116774191104*Dv^8*Ev^14 - ... 527797227747917066718412800*Dv^10*Ev^14 + 2527203853522944884736*Ev^16 - ... 84888033570057947185152*Dv^2*Ev^16 + 5348878696039392485572608*Dv^4*Ev^16 + ... 8425243642070730371235840*Dv^6*Ev^16 + 397591148652169914010828800*Dv^8*Ev^16 - ... 56895597247200386088960*Ev^18 + 186917041024084670939136*Dv^2*Ev^18 - ... 49137685829088932096114688*Dv^4*Ev^18 - 276557573343876291860889600*Dv^6*Ev^18 + ... 732192936896640810221568*Ev^20 + 6704721985334673005346816*Dv^2*Ev^20 + ... 218816625434574528184320000*Dv^4*Ev^20 - 4406564108648813030277120*Ev^22 - ... 49875605619144518113689600*Dv^2*Ev^22 + 7665720829950577921228800*Ev^24); coef(16)=-16*(11 - 5826*Dv^2 + 1342920*Dv^4 - 180090976*Dv^6 + 15747945600*Dv^8 - 937368224256*Dv^10 + ... 38433711134720*Dv^12 - 1077390347083776*Dv^14 + 20100473158533120*Dv^16 - 237224750688239616*Dv^18 + ... 1627514182255509504*Dv^20 - 5605948622949580800*Dv^22 + 7489524376535040000*Dv^24 - 19278*Ev^2 + ... 9048720*Dv^2*Ev^2 - 1792837344*Dv^4*Ev^2 + 207374128128*Dv^6*Ev^2 - 15835111859712*Dv^8*Ev^2 + ... 824154862080000*Dv^10*Ev^2 - 29116666525851648*Dv^12*Ev^2 + 687702879413600256*Dv^14*Ev^2 - ... 10589336542479384576*Dv^16*Ev^2 + 100838944812872761344*Dv^18*Ev^2 - ... 520137620612752343040*Dv^20*Ev^2 + 999173880633360384000*Dv^22*Ev^2 + 14205096*Ev^4 - ... 5760447264*Dv^2*Ev^4 + 956108484864*Dv^4*Ev^4 - 92164771795968*Dv^6*Ev^4 + ... 5906686716610560*Dv^8*Ev^4 - 259099853745070080*Dv^10*Ev^4 + 7613140731654832128*Dv^12*Ev^4 - ... 144228650098539626496*Dv^14*Ev^4 + 1686904336835338567680*Dv^16*Ev^4 - ... 11406966009692222914560*Dv^18*Ev^4 + 35919047904347906113536*Dv^20*Ev^4 - 5815279008*Ev^6 + ... 1971031781376*Dv^2*Ev^6 - 267270075878400*Dv^4*Ev^6 + 20679901481852928*Dv^6*Ev^6 - ... 1053444110624464896*Dv^8*Ev^6 + 36713502401187151872*Dv^10*Ev^6 - 839410767409255022592*Dv^12*Ev^6 + ... 11453371001680095608832*Dv^14*Ev^6 - 81028452974567639482368*Dv^16*Ev^6 + ... 202342263181631721308160*Dv^18*Ev^6 + 1473870722688*Ev^8 - 400912776350208*Dv^2*Ev^8 + ... 43563518065354752*Dv^4*Ev^8 - 2613479579929829376*Dv^6*Ev^8 + 100040764526003552256*Dv^8*Ev^8 - ... 2626241559714923544576*Dv^10*Ev^8 + 45243306187525069996032*Dv^12*Ev^8 - ... 423453240331915870863360*Dv^14*Ev^8 + 1946263742220163860135936*Dv^16*Ev^8 - 243624947166720*Ev^10 + ... 50520829862006784*Dv^2*Ev^10 - 4297784573275103232*Dv^4*Ev^10 + 190762090575120433152*Dv^6*Ev^10 - ... 5063663450641660379136*Dv^8*Ev^10 + 91387930628669174710272*Dv^10*Ev^10 - ... 1153718604326186300473344*Dv^12*Ev^10 + 3079225556639672759746560*Dv^14*Ev^10 + ... 26905533705566208*Ev^12 - 3974406099933782016*Dv^2*Ev^12 + 253774298542765768704*Dv^4*Ev^12 - ... 7693308338116953636864*Dv^6*Ev^12 + 119775785315321360941056*Dv^8*Ev^12 - ... 932321028875262785224704*Dv^10*Ev^12 + 19214402876712866877014016*Dv^12*Ev^12 - ... 1995869940091969536*Ev^14 + 192096876752615374848*Dv^2*Ev^14 - 8326255891891815972864*Dv^4*Ev^14 + ... 154410861123290190053376*Dv^6*Ev^14 - 869668520297020992258048*Dv^8*Ev^14 - ... 33573406201452827435335680*Dv^10*Ev^14 + 98209201387983372288*Ev^16 - ... 5562074622554604306432*Dv^2*Ev^16 + 115154732102634411393024*Dv^4*Ev^16 - ... 1817064098455577136463872*Dv^6*Ev^16 + 35451663521631895673634816*Dv^8*Ev^16 - ... 3093695397194311139328*Ev^18 + 98087015573230706491392*Dv^2*Ev^18 + ... 598859451977997138001920*Dv^4*Ev^18 + 4805287947246523530608640*Dv^6*Ev^18 + ... 58056122998268922691584*Ev^20 - 1180346241408757917548544*Dv^2*Ev^20 - ... 16895362630269298387451904*Dv^4*Ev^20 - 564906472127510693806080*Ev^22 + ... 7510908226870142797086720*Dv^2*Ev^22 + 2155723881603908449075200*Ev^24); coef(17)=(1 - 336*Dv^2 + 39648*Dv^4 - 2038528*Dv^6 + 47851776*Dv^8 - 459841536*Dv^10 + 1194393600*Dv^12 - ... 1008*Ev^2 + 237888*Dv^2*Ev^2 - 21222144*Dv^4*Ev^2 + 797174784*Dv^6*Ev^2 - 12917366784*Dv^8*Ev^2 + ... 83416449024*Dv^10*Ev^2 + 356832*Ev^4 - 49289472*Dv^2*Ev^4 + 2806949376*Dv^4*Ev^4 - ... 65464713216*Dv^6*Ev^4 + 264438743040*Dv^8*Ev^4 - 57915648*Ev^6 + 4053224448*Dv^2*Ev^6 - ... 112117727232*Dv^4*Ev^6 + 2585049956352*Dv^6*Ev^6 + 4544854272*Ev^8 - 113998897152*Dv^2*Ev^8 - ... 1644679987200*Dv^4*Ev^8 - 165919186944*Ev^10 + 1390560804864*Dv^2*Ev^10 + 2212255825920*Ev^12)^2; FLD22=roots(coef); FLD=sqrt([FLD21',FLD22'])*hv/tensor.g(3,3); otherwise error('Invalid spin multiplicity: Analytical equation is not given.'); quit; end FLD1=[]; for n0=1:size(FLD,2) if isreal(FLD(n0))==1 FLD1=[FLD1 FLD(n0)]; end end FLD=sort(FLD1); %%% function M = mkrotmat(theta,phi,psi) % generating a rotation matrix; %function M = mkrotmat(theta,phi,psi) % % M1 = [cphi sphi 0;-sphi cphi 0;0 0 1]; % M2 = [1 0 0;0 cthe sthe;0 -sthe cthe]; % M3 = [cpsi spsi 0;-spsi cpsi 0;0 0 1]; % % M = M3*M2*M1 % M=[cos(phi)*cos(psi)-cos(theta)*sin(phi)*sin(psi) ... sin(phi)*cos(psi) + cos(theta)*cos(phi)*sin(psi) ... sin(theta)*sin(psi); -cos(phi)*sin(psi)-cos(theta)*sin(phi)*cos(psi) ... -sin(phi)*sin(psi) + cos(theta)*cos(phi)*cos(psi) ... sin(theta)*cos(psi); sin(theta)*sin(phi) ... -sin(theta)*cos(phi) ... cos(theta)]; %%% function M = rotmat(theta,phi,psi,tn) % Unitary transformation of a tensor, tn %function M = rotmat(theta,phi,psi,tn) um=mkrotmat(theta,phi,psi); tn1=um*tn*um'; M=(tn1+tn1')/2; for i=1:3 for j=1:3 if abs(M(i,j))