There are span tables here, but the only go up to a 2.4m opening:
http://www.fordtimbers.com.au/dpr_span_tables.htm
There are LVL span tables
here, and depending on your Roof Load Width, for a span of 3.5m, you'd need at least a 240x63, with an RLW of 2.4m, up to a 300x63 for an RLW of 7.2m.