#Homework by Mike Murr
#OK to post
#hw17
read(`C17.txt`);

RseqFF(24,10);

#with(NumberTheory);

CheckDeligne:=proc(N) local i, p, tauFunc, numerVal, denomVal, quotientVal, smallQuotient, largeQuotient, smallQuotP, largeQuotP;

tauFunc:=RseqFF(24,N);

smallQuotient:=1;

largeQuotient:=0;

for p from 2 to N do
  if isprime(p) then
#    print(p);
    numerVal:=tauFunc[p];
#    print(numerVal);
    denomVal:=evalf(2*p^(11/2));
#    print(denomVal);
    quotientVal:=abs(numerVal)/denomVal;
#    print(quotientVal);
    if quotientVal < smallQuotient then
      smallQuotient:=quotientVal;
      smallQuotP:=p;
      print(smallQuotP, smallQuotient);
    fi;
    if quotientVal > largeQuotient then
      largeQuotient:=quotientVal;
      largeQuotP:=p;
      print(largeQuotP, largeQuotient);
    fi;
  fi;
od;

#print(smallQuotP, smallQuotient);

#print(largeQuotP, largeQuotient);

end proc;

#CheckDeligne(2000);

#CheckDeligne(7000);

CheckDeligne(15000);

# From the output:
#
#                     7589, 0.9802666258
#                     7993, 0.0003198235674
#
# Yes, with larger N, we got closer to the upper bound.