lfundual

Function: lfundual
Section: l_functions
C-Name: lfundual
Prototype: Gb
Help: lfundual(L): creates the Ldata structure (without
 initialization) corresponding to the dual L-function of L.
Doc: creates the \kbd{Ldata} structure (without initialization) corresponding
 to the dual L-function $\hat{L}$ of $L$. If $k$ and $\varepsilon$ are
 respectively the weight and root number of $L$, then the following formula
 holds outside poles, up to numerical errors:
 $$\Lambda(L, s) = \varepsilon \Lambda(\hat{L}, k - s).$$

 \bprog
 ? L = lfunqf(matdiagonal([1,2,3,4]));
 ? eps = lfunrootres(L)[3]; k = L[4];
 ? M = lfundual(L); lfuncheckfeq(M)
 %3 = -127
 ? s= 1+Pi*I;
 ? a = lfunlambda(L,s);
 ? b = eps * lfunlambda(M,k-s);
 ? exponent(a - b)
 %7 = -130
 @eprog