Here it is from Dokchitser in Magma:

> L:=LSeries(HilbertClassField(QuadraticField(145)) : Method:="Artin");
> L`prod;
[
  <L-series of Riemann zeta function, 1>,
  <L-series of Artin representation of Number Field with defining polynomial x^8 - 
    636*x^6 + 135214*x^4 - 11109740*x^2 + 290532025 over the Rational Field with
    character ( 1, 1, 1, -1, -1 ) and conductor 5, 1>,
  <L-series of Artin representation of Number Field with defining polynomial x^8 - 
    636*x^6 + 135214*x^4 - 11109740*x^2 + 290532025 over the Rational Field with
    character ( 1, 1, -1, -1, 1 ) and conductor 145, 1>,
  <L-series of Artin representation of Number Field with defining polynomial x^8 - 
    636*x^6 + 135214*x^4 - 11109740*x^2 + 290532025 over the Rational Field with
    character ( 1, 1, -1, 1, -1 ) and conductor 29, 1>,
  <L-series of Artin representation of Number Field with defining polynomial x^8 - 
    636*x^6 + 135214*x^4 - 11109740*x^2 + 290532025 over the Rational Field with
    character ( 2, -2, 0, 0, 0 ) and conductor 145, 2>
]
> L5:=L`prod[5][1];
> CheckFunctionalEquation(L5); // LCfRequired(L5) demands 161 terms
1.57772181044202361082345713057E-30
> [<p,-Integers()!Coefficient(EulerFactor(L5,p),1)> : p in PrimesUpTo(100)];
[ <2, 0>, <3, 0>, <5, -1>, <7, 0>, <11, 0>, <13, 0>, <17, 0>, <19, 0>, <23, 0>, 
  <29, -1>, <31, 0>, <37, 0>, <41, 0>, <43, 0>, <47, 0>, <53, 0>, <59, -2>, <61, 0>,
  <67, 0>, <71, -2>, <73, 0>, <79, 0>, <83, 0>, <89, 0>, <97, 0> ]

These are the same as your ap(p), essentially.