diff --git a/stim/math/spharmonics.h b/stim/math/spharmonics.h
index 266af7d..c51ee91 100644
--- a/stim/math/spharmonics.h
+++ b/stim/math/spharmonics.h
@@ -25,8 +25,20 @@ protected:
 	//calculate the value of the SH basis function (l, m) at (theta, phi)
 		//here, theta = [0, PI], phi = [0, 2*PI]
 	double SH(int l, int m, double theta, double phi){
-		std::complex<T> result = boost::math::spherical_harmonic(l, m, phi, theta);
-		return result.imag() + result.real();
+		//std::complex<T> result = boost::math::spherical_harmonic(l, m, phi, theta);
+		//return result.imag() + result.real();
+
+		//this calculation is based on calculating the real spherical harmonics:
+		//		https://en.wikipedia.org/wiki/Spherical_harmonics#Addition_theorem
+		if (m < 0) {
+			return sqrt(2.0) * pow(-1, m) * boost::math::spherical_harmonic(l, abs(m), phi, theta).imag();
+		}
+		else if (m == 0) {
+			return boost::math::spherical_harmonic(l, m, phi, theta).real();
+		}
+		else {
+			return sqrt(2.0) * pow(-1, m) * boost::math::spherical_harmonic(l, m, phi, theta).real();
+		}
 	}
 
 	unsigned int coeff_1d(unsigned int l, int m){
--
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