• LfunctionsAndModularFormsII
• CentralValues
• GP.scripts

{D1(H)=local(H3,t,m,n); H3=sqrtint(H^2\3); t=O(q^(H^2\12));
 for(m=-H,H,if(gcd(m,6)==1,for(n=-H3,H3,
   if(n%2==0,if(n%4==0,
     if((-1)^(n\4)*kronecker(-24,m)==1,t+=m*q^((m^2+3*n^2-1)/12)),
     if((-1)^((n-2)/4)*kronecker(24,m)==1,t+=n*q^((m^2+3*n^2-1)/12)));))));t}

{D2(H)=local(H3,t,m,n); H3=sqrtint(H^2\3); t=O(q^(H^2\12));
 for(m=-H,H,if(gcd(m,6)==2,for(n=-H3,H3,
  if(n%2==1,if(m%4==0,
   if(kronecker(8,n)*psi1(m/4)==1,t+=m*q^((m^2+3*n^2-7)/12)),
   if(kronecker(-8,n)==kronecker(12,m/2),t+=n*q^((m^2+3*n^2-7)/12)))))));t/2}

{F1(H)=local(t,m,n);t = O(q^(H^2\24));
  for(m=0,H, if((m%3)&&(m%4), for(n=-H\3,H\3, if(n%4,
    c=(m+n)%8; if((c==3)||(c==5), t += m*n*q^((m^2+9*n^2-13)/24)/2)))));t}

{F2(H)=local(t,m,n); t=O(q^(H^2\24));
 for(m=-H,H,if(gcd(m,6)==1&&kronecker(-24,m)==1,
  for(n=-H,H,if(gcd(n,12)==2&&kronecker(-4,n/2)==1,
      t-=kronecker(12,m)*kronecker(-3,n)*(m^2-n^2)*q^((m^2+n^2-5)/24)/3))));t}

{F3(L)=local(A1); A1=O(q^(L^2));
 forstep(a=1,L,2,forstep(b=-2*(L\2)-2,L,2,\\ b is even
  if(a%3==0 && b%3!=0,w=kronecker(-4,a/3);
     if(abs(b)%12==2 || abs(b)%12==4,,w=-w);
     A1+=4*w*a*abs(b)*q^(a^2+b^2));
  if(a%3!=0 && b%3==0,if(b%12==0,w=kronecker(12,a),w=-kronecker(12,a));
     A1+=w*(a^2-b^2)*q^(a^2+b^2))));A1}

{F4(L)=local(A1); A1=O(q^(L^2));
 forstep(a=1,L,2,forstep(b=0,L,2,w2=kronecker(12,a);w1=kronecker(-4,a);
  if(a%3!=0 && b%3!=0,
     if(b%12==2 || b%12==4,,w1=-w1);if(b%12==2 || b%12==10,,w2=-w2);
     A1+=(w1*4*a*b+w2*(a^2-b^2))*q^(a^2+b^2)))); A1}

{F5(L)=local(A1,A2,w); A1=O(q^(L^2)); A2=O(q^(L^2));
 forstep(a=4,L,4,forstep(b=1,L,2,
   if(a%24==4,w=kronecker(-24,b)); if(a%24==8,w=kronecker(-24,b));
   if(a%24==16,w=-kronecker(-24,b)); if(a%24==20,w=-kronecker(-24,b));
   if(a%3 && b%3,A1+=w*2*a*b*q^(a^2+b^2))));
 forstep(a=3,L,6,forstep(b=2,sqrtint(L^2/2),2,
   if(b%12==2,w=-1); if(b%12==10,w=-1); if(b%12==4,w=+1); if(b%12==8,w=+1);
   if(b%3,A2+=w*(a^2-2*b^2)*q^(a^2+2*b^2)))); A1+A2}

{S1(L)=local(L2,L3,w,A); L2=L^2; L3=ceil(sqrt(L2/3)); A=O(q^(L^2));
 forstep(a=2,L,4,forstep(b=-L3-1+L3%2,L3,2,\\ b is 1 mod 2 *
                  if((a+b)%3==0 && b%3,w=1;
                   if(a%8==2,w=kronecker(24,b),w=-kronecker(24,b));
                   A+=w*(a+b)/3*q^(a^2+3*b^2))));
 forstep(b=3,L3,6,forstep(a=2,L,4,
   if(a%3,A-=kronecker(12,a/2)*kronecker(-8,b/3)*(2*b)/3*q^(a^2+3*b^2))));A}

{S2(L)=local(L3,w,B); L3=ceil(sqrt(L^2/3)); B=O(q^(L^2));
 forstep(a=1,L,2,forstep(b=(-L3-4)+(-L3)%4+(2*(-L3))%4-2,L3,4,\\ b is 2 (4)
                  if((a+b)%3==0 && b%3,
                   if(abs(b)%24==2,if(kronecker(-8,a)==-1,w=-1,w=1));
                   if(abs(b)%24==10,if(kronecker(-8,a)==1,w=-1,w=1));
                   if(abs(b)%24==14,if(kronecker(-8,a)==1,w=-1,w=1));
                   if(abs(b)%24==22,if(kronecker(-8,a)==-1,w=-1,w=1));
                   B+=w*(a+b)/3*q^(a^2+3*b^2))));
 forstep(b=6,L3,12,forstep(a=1,L,2,
   if(a%3,w=kronecker(24,a)*kronecker(-4,b/6);B+=w*(2*b)/3*q^(a^2+3*b^2))));B}