Geodesic
A few factors from the Euler product are sufficient for calculating the zeta function with high precision
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Analytic number theory, Tome 299 (2017), pp. 192-202

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The paper demonstrates by numerical examples a nontraditional way to get high precision values of Riemann's zeta function inside the critical strip by using the functional equation and the factors from the Euler product corresponding to a very small number of primes. For example, the three initial primes produce more than 50 correct decimal digits of $\zeta (1/4+10\kern 1pt\mathrm i)$.
Keywords: Riemann's zeta function, functional equation
Mots-clés : Euler product. 
@article{TM_2017_299_a11,
     author = {Yu. V. Matiyasevich},
     title = {A few factors from the {Euler} product are sufficient for calculating the zeta function with high precision},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {192--202},
     publisher = {mathdoc},
     volume = {299},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2017_299_a11/}
}
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Yu. V. Matiyasevich. A few factors from the Euler product are sufficient for calculating the zeta function with high precision. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Analytic number theory, Tome 299 (2017), pp. 192-202. http://geodesic.mathdoc.fr/item/TM_2017_299_a11/