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The optical properties of square nanospirals made of gold have been investigated numerically in the hundred terahertz range as a function of the geometrical parameters of the nanospirals. It is shown that the permittivity values of the nanospirals originate from the longitudinal surface plasmon resonances of the arms composing the nanospirals. A magnetic resonance was also observed whose magnitude and position increased with the number of winding. Above three windings the gold nanospirals exhibited negative values of the real part of the permeability above 400 THz.