diff --git a/src/bls12_381/mod.rs b/src/bls12_381/mod.rs
index 4c2a76f..341df67 100644
--- a/src/bls12_381/mod.rs
+++ b/src/bls12_381/mod.rs
@@ -93,6 +93,10 @@ impl Engine for Bls12 {
             ell(&mut f, coeffs.next().unwrap(), &p.0);
         }
 
+        if BLS_X_IS_NEGATIVE {
+            f.conjugate();
+        }
+
         f
     }
 
@@ -148,6 +152,7 @@ impl Engine for Bls12 {
                 y2 = y3;
                 y2.frobenius_map(1);
                 y1.mul_assign(&y2);
+
                 Some(y1)
             },
             None => None
diff --git a/src/bls12_381/tests/mod.rs b/src/bls12_381/tests/mod.rs
index 08de508..1b3d521 100644
--- a/src/bls12_381/tests/mod.rs
+++ b/src/bls12_381/tests/mod.rs
@@ -1,6 +1,57 @@
 use super::*;
 use ::*;
 
+#[test]
+fn test_pairing_result_against_relic() {
+    /*
+    Sent to me from Diego Aranha (author of RELIC library):
+
+    1250EBD871FC0A92 A7B2D83168D0D727 272D441BEFA15C50 3DD8E90CE98DB3E7 B6D194F60839C508 A84305AACA1789B6
+    089A1C5B46E5110B 86750EC6A5323488 68A84045483C92B7 AF5AF689452EAFAB F1A8943E50439F1D 59882A98EAA0170F
+    1368BB445C7C2D20 9703F239689CE34C 0378A68E72A6B3B2 16DA0E22A5031B54 DDFF57309396B38C 881C4C849EC23E87
+    193502B86EDB8857 C273FA075A505129 37E0794E1E65A761 7C90D8BD66065B1F FFE51D7A579973B1 315021EC3C19934F
+    01B2F522473D1713 91125BA84DC4007C FBF2F8DA752F7C74 185203FCCA589AC7 19C34DFFBBAAD843 1DAD1C1FB597AAA5
+    018107154F25A764 BD3C79937A45B845 46DA634B8F6BE14A 8061E55CCEBA478B 23F7DACAA35C8CA7 8BEAE9624045B4B6
+    19F26337D205FB46 9CD6BD15C3D5A04D C88784FBB3D0B2DB DEA54D43B2B73F2C BB12D58386A8703E 0F948226E47EE89D
+    06FBA23EB7C5AF0D 9F80940CA771B6FF D5857BAAF222EB95 A7D2809D61BFE02E 1BFD1B68FF02F0B8 102AE1C2D5D5AB1A
+    11B8B424CD48BF38 FCEF68083B0B0EC5 C81A93B330EE1A67 7D0D15FF7B984E89 78EF48881E32FAC9 1B93B47333E2BA57
+    03350F55A7AEFCD3 C31B4FCB6CE5771C C6A0E9786AB59733 20C806AD36082910 7BA810C5A09FFDD9 BE2291A0C25A99A2
+    04C581234D086A99 02249B64728FFD21 A189E87935A95405 1C7CDBA7B3872629 A4FAFC05066245CB 9108F0242D0FE3EF
+    0F41E58663BF08CF 068672CBD01A7EC7 3BACA4D72CA93544 DEFF686BFD6DF543 D48EAA24AFE47E1E FDE449383B676631
+    */
+
+    assert_eq!(Bls12::pairing(G1::one(), G2::one()), Fq12 {
+        c0: Fq6 {
+            c0: Fq2 {
+                c0: Fq::from_str("2819105605953691245277803056322684086884703000473961065716485506033588504203831029066448642358042597501014294104502").unwrap(),
+                c1: Fq::from_str("1323968232986996742571315206151405965104242542339680722164220900812303524334628370163366153839984196298685227734799").unwrap()
+            },
+            c1: Fq2 {
+                c0: Fq::from_str("2987335049721312504428602988447616328830341722376962214011674875969052835043875658579425548512925634040144704192135").unwrap(),
+                c1: Fq::from_str("3879723582452552452538684314479081967502111497413076598816163759028842927668327542875108457755966417881797966271311").unwrap()
+            },
+            c2: Fq2 {
+                c0: Fq::from_str("261508182517997003171385743374653339186059518494239543139839025878870012614975302676296704930880982238308326681253").unwrap(),
+                c1: Fq::from_str("231488992246460459663813598342448669854473942105054381511346786719005883340876032043606739070883099647773793170614").unwrap()
+            }
+        },
+        c1: Fq6 {
+            c0: Fq2 {
+                c0: Fq::from_str("3993582095516422658773669068931361134188738159766715576187490305611759126554796569868053818105850661142222948198557").unwrap(),
+                c1: Fq::from_str("1074773511698422344502264006159859710502164045911412750831641680783012525555872467108249271286757399121183508900634").unwrap()
+            },
+            c1: Fq2 {
+                c0: Fq::from_str("2727588299083545686739024317998512740561167011046940249988557419323068809019137624943703910267790601287073339193943").unwrap(),
+                c1: Fq::from_str("493643299814437640914745677854369670041080344349607504656543355799077485536288866009245028091988146107059514546594").unwrap()
+            },
+            c2: Fq2 {
+                c0: Fq::from_str("734401332196641441839439105942623141234148957972407782257355060229193854324927417865401895596108124443575283868655").unwrap(),
+                c1: Fq::from_str("2348330098288556420918672502923664952620152483128593484301759394583320358354186482723629999370241674973832318248497").unwrap()
+            }
+        }
+    });
+}
+
 fn test_vectors<G: CurveProjective, E: EncodedPoint<Affine=G::Affine>>(expected: &[u8])
 {
     let mut e = G::zero();