default(realprecision,38);
K=bnfinit(x^2+31);bnrL1(bnrinit(K,1,1))
K=bnfinit(x^2-3);
bnrL1(bnrinit(K,5,1),,5)
bnrL1(bnrinit(K,[5,[1,0]],1),,5)
bnrL1(bnrinit(K,[5,[1,1]],1),,5)
K=bnfinit(x^2-168);\\#1601
bnrL1(bnrinit(K,[6,[1,1]],1),,5)

P=x^5-x^4-5*x^3+4*x^2+3*x-1;
S=x^10-26*x^8+233*x^6-832*x^4+1024*x^2-401;
bnf=bnfinit(a^2-401*25);
cond=rnfconductor(bnf,P);
bnr=bnrinit(bnf,cond[1],1);
real(bnrL1(bnr,cond[3],1))
