Abstract: We perform a systematic analysis of the J/psi -> gamma pi(0)pi(0) and -> gamma(KSKS0)-K-0 partial waves measured by BESIII. We use a large set of amplitude parametrizations to reduce the model bias. We determine the physical properties of seven scalar and tensor resonances in the 1-2.5 GeV mass range. These include the well known f(0)(1500) and f(0)(1710), that are considered to be the primary glueball candidates. The hierarchy of resonance couplings determined from this analysis favors the latter as the one with the largest glueball component.