diff --git a/src/navier-stokes.c b/src/navier-stokes.c
index 51d198c..ce07077 100644
--- a/src/navier-stokes.c
+++ b/src/navier-stokes.c
@@ -553,8 +553,8 @@ double compute_alpha(
   num=0.;
   denom=0.;
 
-  for(kx=-K1;kx<=K1;kx++){
-    for(ky=-K2;ky<=K2;ky++){
+  for(kx=0;kx<=K1;kx++){
+    for(ky=(kx>0 ? -K2 : 1);ky<=K2;ky++){
       num+=L*L/4/M_PI/M_PI*(kx*kx+ky*ky)*getval_sym(g, kx,ky,K2)*conj(getval_sym(u, kx,ky,K2));
       denom+=__real__ (kx*kx+ky*ky)*(kx*kx+ky*ky)*getval_sym(u, kx,ky,K2)*conj(getval_sym(u, kx,ky,K2));
     }
@@ -572,12 +572,12 @@ double compute_energy(
 ){
   int kx,ky;
   double out=0.;
-  for(kx=-K1;kx<=K1;kx++){
-    for (ky=-K2;ky<=K2;ky++){
+  for(kx=0;kx<=K1;kx++){
+    for(ky=(kx>0 ? -K2 : 1);ky<=K2;ky++){
       out+=__real__ (getval_sym(u, kx,ky,K2)*conj(getval_sym(u, kx,ky,K2)));
     }
   }
-  return out;
+  return 2*out;
 }
 
 // compute enstrophy
@@ -589,12 +589,12 @@ double compute_enstrophy(
 ){
   int kx,ky;
   double out=0.;
-  for(kx=-K1;kx<=K1;kx++){
-    for (ky=-K2;ky<=K2;ky++){
+  for(kx=0;kx<=K1;kx++){
+    for(ky=(kx>0 ? -K2 : 1);ky<=K2;ky++){
       out+=__real__ (4*M_PI*M_PI/L/L*(kx*kx+ky*ky)*getval_sym(u, kx,ky,K2)*conj(getval_sym(u, kx,ky,K2)));
     }
   }
-  return out;
+  return 2*out;
 }