/*** EXAMPLE: Eisenstein series G_k, k>2 even ***/
/*** v1.2, July 2013, questions to tim.dokchitser@bristol.ac.uk ***/
/*** ***/
/*** type \rex-eisen or read("ex-eisen") at gp prompt to run this ***/
read("computel"); \\ read the ComputeL package
\\ and set the default values
default(realprecision,40); \\ set working precision; used throughout
K = 16; \\ Our modular form is G_K with this K
\\ may change this to any even K
conductor = 1; \\ exponential factor
gammaV = [0,1]; \\ list of gamma-factors
weight = K; \\ L(s)=sgn*L(weight-s)
sgn = (-1)^(K/2); \\ sign in the functional equation
\\ It has a simple pole in s=K
Lpoles = [K];
Lresidues = [(-1)^(K/2)*sqrt(Pi)*bernfrac(K)/K];
initLdata("sigma(k,K-1)"); \\ initialize L-series
\\ Coefficients given by the divisor function
print("EXAMPLE: L-function associated to the modular form G_",K," of weight ",K);
print(" coefficients = divisor function sigma(n,",K-1,")");
print(" with ",default(realprecision)," digits precision");
print("Verifying functional equation. Error: ",errprint(checkfeq()));
print("L(1) = ",lval = L(1));
print(" (check) = ",lval2 = L(1,1.1)," (err=",errprint(lval-lval2),")");