How to calculate temperature resistance for Ni-RTD
Updated with a better calculator 

Use an online calculator like this with R = 1000 ohm, there is a NI-RTD with a temperature coefficient of 0.00618 that I think it is an approximation of the 0.006178 that you have, it should be the same material.   

If you need a polynomial approximation use together with this tool 

For samples at 0, 40, 80, 120 degrees the formula is:
R = 1000(1 + 0.00549577t + 0.000006156t^2 + 0.000000006732t^3)

Or use the values from the table to find A, B and C in the CALLENDAR-VAN DUSEN formula.

Choose the sample points close to your interest area

It's true that there are errors of a few percents with the linearized formula, the maximum error is somewhere around 40 degrees.