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Nowadays, more and more RDF data is becoming available on the Semantic Web. While the Semantic Web is generally incomplete by nature, on certain topics, it already contains complete information and thus, queries may return all answers that exist in reality. In this paper we develop a technique to check query completeness based on RDF data annotated with completeness information, taking into account data-specific inferences that lead to an inference problem which is $\Pi^P_2$-complete. We then identify a practically relevant fragment of completeness information, suitable for crowdsourced, entity-centric RDF data sources such as Wikidata, for which we develop an indexing technique that allows to scale completeness reasoning to Wikidata-scale data sources. We verify the applicability of our framework using Wikidata and develop COOL-WD, a completeness tool for Wikidata, used to annotate Wikidata with completeness statements and reason about the completeness of query answers over Wikidata. The tool is available at http://cool-wd.inf.unibz.it/.