Scores on the math portion of the SAT are believed to be normally distributed and range from $200$ to $800.$ A researcher from the admissions department at the University of New Hampshire is interested in estimating the mean math SAT scores of the incoming class with $95\%$ confidence. How large a sample should she take to ensure that the margin of error is below $29?($You may find it useful to reference the z table. Round up final answer to nearest whole number.$)$