diff --git a/sunscreen_tfhe/src/math/fft/negacyclic/mod.rs b/sunscreen_tfhe/src/math/fft/negacyclic/mod.rs
index 540c79a1f..585f4c7ab 100644
--- a/sunscreen_tfhe/src/math/fft/negacyclic/mod.rs
+++ b/sunscreen_tfhe/src/math/fft/negacyclic/mod.rs
@@ -60,10 +60,13 @@ where
 
         let two_pi = T::from(PI).unwrap() * T::from(2.0).unwrap();
 
-        let w_2n = (Complex::from(two_pi / n_2) * Complex::i()).exp();
-
         let twist = (0..k)
-            .map(|x| w_2n.powf(T::from(x).unwrap()))
+            .map(|x| {
+                let x = T::from(x).unwrap();
+                let (s, c) = (two_pi * x / n_2).sin_cos();
+
+                Complex::new(c, s)
+            })
             .collect::<Vec<_>>();
 
         let twist_inv = twist
@@ -76,7 +79,7 @@ where
             let a_a_inv = a * b;
             let err = a_a_inv - Complex::one();
 
-            err.re.abs() < T::from(1e-12).unwrap() && err.im.abs() < T::from(1e-12).unwrap()
+            err.re.abs() < T::from(1e-15).unwrap() && err.im.abs() < T::from(1e-15).unwrap()
         }));
 
         Self {
diff --git a/sunscreen_tfhe/src/math/polynomial.rs b/sunscreen_tfhe/src/math/polynomial.rs
index 94c998adc..74483156f 100644
--- a/sunscreen_tfhe/src/math/polynomial.rs
+++ b/sunscreen_tfhe/src/math/polynomial.rs
@@ -321,7 +321,7 @@ mod tests {
             let a = Polynomial::new(&a);
             let b = (0..n)
                 .map(|_| {
-                    let signed = (rand::thread_rng().next_u64() % 32).reinterpret_as_signed() - 16;
+                    let signed = (rand::thread_rng().next_u64() % (0x1 << 16)).reinterpret_as_signed() - 16;
 
                     signed.reinterpret_as_unsigned()
                 })
@@ -346,7 +346,7 @@ mod tests {
 
             for (a, e) in actual.coeffs().iter().zip(expected.coeffs().iter()) {
                 let err = normalized_torus_distance(a, e).abs();
-                assert!(err < 1e-12);
+                assert!(err < 1e-9);
             }
         }
     }