  We present measurements of three distinctive state-(in)dependent wavelengths
for the $^1\text{S}_{0}-^3\text{P}_{0}$ clock transition in $^{174}\text{Yb}$
atoms. Specifically, we determine two magic wavelengths at $652.281(21)\,$THz
and $542.50205(19)\,$THz, where the differential light shift on the
$^1\text{S}_{0}-^3\text{P}_{0}$ clock transition vanishes, and one tune-out
wavelength at $541.8325(5)\,$THz, where the polarizability of the
$^1\text{S}_{0}$ ground state exhibits a zero crossing. The two new magic
wavelengths are identified by spectroscopically interrogating cold
$^{174}\text{Yb}$ atoms on the clock transition in a one-dimensional optical
lattice. The ground-state tune-out wavelength is determined via a parametric
heating scheme. With a simple empirical model, we then extrapolate the ground
and excited state polarizability over a broad range of wavelengths in the
visible spectrum.
