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# Sage's E.aplist(100) returns a list of the Fourier coefficients for
# p<100. For the aplist files, we want to replace the coefficient for
# p|N with the W-eigenvalue (the root number) and append the
# W-eigenvalues for p|N, p>100. Not relevant for making LMFDBupload
# files.
from sage.all import prime_range
def wstr(n, w): # str(n) with enough spaces prepended to give width w
a = str(n)
if len(a) < w:
a = ' ' * (w - len(a)) + a
return a
def my_ap(E, D, p):
if p.divides(D):
return E.root_number(p)
return E.ap(p)
def my_ap_str(E, D, p):
if p.divides(D):
a = E.root_number(p)
if a == 1:
if p > 23:
return ' +'
return ' +'
if p > 23:
return ' -'
return ' -'
if p > 23:
return wstr(E.ap(p), 3)
return wstr(E.ap(p), 2)
def my_aplist(E):
D = E.discriminant()
ap = [my_ap_str(E, D, p) for p in prime_range(100)]
qlist = D.support()
for q in qlist:
if q > 100:
if E.root_number(q) == 1:
ap.append('+('+str(q)+')')
else:
ap.append('-('+str(q)+')')
return ' '.join(ap)
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