CharPolyFromTraces:=function(pp,S,x)
dd:=#pp;
ans:=x^dd;
s:=[pp[1]];
ans:=ans-s[1]*x^(dd-1);
if dd gt 1 then 
for k:=2 to dd do
s[k]:=0;
for l:=1 to k-1 do 
s[k]:=s[k]+ (-1)^(l-1) * s[k-l]*pp[l];
end for;
s[k]:=s[k]+(-1)^(k-1) *pp[k];
s[k]:=(1/k)*s[k];
ans:=ans+(-1)^(k)*s[k]*x^(dd-k);
end for;
end if;
return ans;
end function;

TraceSequence:=function(G,A,chi,K)
f:=ClassMap(G);
eQ:=Order(A);
return [K!chi[f(A^k)] : k in [1..chi[1]]];
end function;




n:=function(G,alpha,A,chi)
eQ:=Order(A);
K<z>:=CyclotomicField(#G);
t := z^Round(#G/eQ);
p:=TraceSequence(G,A,chi,K);
S<x>:=PolynomialRing(K);
rootlist:=Roots(CharPolyFromTraces(p,S,x));
ans:=0;
for k :=1 to #rootlist do
if t^alpha eq rootlist[k][1] then 
ans:= rootlist[k][2];
end if;
end for;
return ans;
end function;







FractionalPart:=function(x)
return x-Floor(x);
end function;





CW:= function(G,gprime,T,CCL,M,m,S)
H0mK:=[];
e:=[Order(M[j]) : j in [1..#M]];
for i:=1 to #CCL do
H0mK[i]:=(2*m-1)*(gprime-1)*T[i][1];
for j:=1 to #M do 
for alpha:=0 to e[j]-1 do 
H0mK[i]:=H0mK[i]+( (m-1)*(1-1/e[j]) + FractionalPart( (m-1-alpha)/e[j]) )*n(G,alpha,M[j],T[i]);
end for;
end for;
if m eq 1 then 
if i eq 1 then 
H0mK[i]:=H0mK[i]+1;
end if;
end if;
end for;
chim:=Character(GModule(G,S,m));
Sm:=Decomposition(T,chim);
Im:=[Sm[j]-H0mK[j] : j in [1..#CCL]];
print "S_m="; print Sm; print "\n";
print "H^0(C,mK)="; print H0mK;print "\n";
print "I_m=";
return Im;
end function;