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England, set a target of 481 in their second innings, were 315 for nine at stumps with Matt Prior 110 not out and Monty Panesar unbeaten on two, denying the Black Caps an historic series win.
Kane Williamson was the pick of the New Zealand bowlers with four for 44.
New Zealand have only won three of 32 series against England. The last time was in England in 1999.