$$ \eta(\tau) = e^{2\pi i \tau/12}\prod_{n=1}^\infty \big(1-q^n\big) $$$$ \eta(\tau) = e^{2\pi i \tau/24}\prod_{n=1}^\infty \big(1-q^n\big) $$ where $$ q = e^{2\pi i \tau} $$ as Pietro said.
corrected the formula for eta -- the factor should be a 24th root of unity
Dustin Clausen
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