diff --git a/acb_dirichlet/platt_local_hardy_z_zeros.c b/acb_dirichlet/platt_local_hardy_z_zeros.c
index 0a3f62fd..489ef93c 100644
--- a/acb_dirichlet/platt_local_hardy_z_zeros.c
+++ b/acb_dirichlet/platt_local_hardy_z_zeros.c
@@ -1373,7 +1373,7 @@ _create_heuristic_context(const fmpz_t n, slong prec)
     {
         goto finish;
     }
-    else if (_fmpz_cmp_a_10exp_b(n, 1, 7) < 0)
+    else if (_fmpz_cmp_a_10exp_b(n, 1, 7) <= 0)
     {
         A = 8;
         B = 4096;
@@ -1385,7 +1385,7 @@ _create_heuristic_context(const fmpz_t n, slong prec)
         dh = 189.300555621 + -18.9197620910*x + 0.830573279739*x*x;
         dH = 0.996344708432 + 0.00726343756987*x + 0.000214553523479*x*x;
     }
-    else if (_fmpz_cmp_a_10exp_b(n, 1, 17) < 0)
+    else if (_fmpz_cmp_a_10exp_b(n, 1, 17) <= 0)
     {
         A = 8;
         B = 4096;
@@ -1397,17 +1397,17 @@ _create_heuristic_context(const fmpz_t n, slong prec)
         dh = 94.8311227685 + -0.883336123977*x + 0.0556261501085*x*x;
         dH = 1.18099035487 + -0.0119992923413*x + 0.00073741022749*x*x;
     }
-    else if (_fmpz_cmp_a_10exp_b(n, 1, 22) < 0)
+    else if (_fmpz_cmp_a_10exp_b(n, 1, 37) <= 0)
     {
         A = 16;
         B = 8192;
         Ns_max = 300;
-        sigma_interp = 19;
-        dlogJ = -0.506132895307 + 0.497565124541*x + 2.25705259466e-06*x*x;
-        dK = 103.630048145 + -0.867460371390*x + 0.00106534037344*x*x;
-        dgrid = 4085.55616952 + -1.36695690825*x + -0.0198932963863*x*x;
-        dh = 142.523364391 + -0.057841628146*x + 0.0157997314814*x*x;
-        dH = 0.727682145349 + -0.00353076385259*x + 0.000111471602416*x*x;
+        sigma_interp = _fmpz_cmp_a_10exp_b(n, 1, 27) < 0 ? 19 : 17;
+        dlogJ = -0.510731356439 + 0.497749405271*x + 4.7480897930e-07*x*x;
+        dK = 98.3296668968 + -0.629042293257*x + -0.00158584251152*x*x;
+        dgrid = 3810.92686930 + 9.86688705118*x + -0.132241869233*x*x;
+        dh = 189.640536974 + -1.94782986530*x + 0.0342403597641*x*x;
+        dH = 0.897872657566 + -0.0100363606454*x + 0.000170869048778*x*x;
     }
     else
     {