Left-arm spinner Ajaz Patel, who has not been a regular part of the team but played the second Test against England, said there is no negativity in the team.
Williamson was forced to miss the second Test against England due to an elbow injury and Tom Latham had led New Zealand to a comfortable eight-wicket win, which had sealed a series triumph for the visitors.
New Zealand made as many as six changes for the ongoing second Test, some forced and some rotated ahead of the World Test Championship final against India in Southampton from June 18.
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Boult, who missed out on the first Test against England as he opted to spend time with his family after the suspension of the IPL in May, was also set to sit out the second match as well.
Replying to England's 303 all out, New Zealand was 229-3 after the unexpected dismissal of Will Young on 82 off the final ball of the day.
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England vs New Zealand 2nd Test Day 1 Live Streaming: When and where to watch Edgbaston Test in India
New Zealand have already been bolstered by the arrival of left-arm pace bowler Trent Boult, who is likely to feature in the second Test.
ICC match referee Chris Broad imposed the sanction after Joe Root's side was ruled to be two overs short of the target after time allowances were taken into consideration.
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Hesson says he is keenly looking forward to how the India top-order will fare against the swinging ball in Southampton when the cross breeze comes into play
Left-handed opener Burns hit 16 fours and one six before he was last man out, caught behind off Southee for 132, as the home team was bowled out for 275.
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