diff --git a/acb_dirichlet/conrey_log.c b/acb_dirichlet/conrey_log.c
index 15040b26..d7a520f9 100644
--- a/acb_dirichlet/conrey_log.c
+++ b/acb_dirichlet/conrey_log.c
@@ -11,6 +11,7 @@
     (at your option) any later version.  See <http://www.gnu.org/licenses/>.
 */
 
+#include "dlog.h"
 #include "acb_dirichlet.h"
 
 /* TODO: use dlog module instead of n_discrete_log_bsgs */
@@ -27,7 +28,8 @@ acb_dirichlet_conrey_log(acb_dirichlet_conrey_t x, const acb_dirichlet_group_t G
       {
         ulong m2 = (x->log[0]) ? -m % G->q_even : m % G->q_even;
         if (G->P[1].dlog == NULL)
-            x->log[1] = n_discrete_log_bsgs(m2, 5, G->q_even);
+            x->log[1] = dlog_mod2e_1mod4(m2, G->P[1].e,
+                    nmod_inv(5, G->P[1].pe), G->P[1].pe);
         else
             x->log[1] = dlog_precomp(G->P[1].dlog, m2);
       }
diff --git a/acb_dirichlet/test/t-conrey.c b/acb_dirichlet/test/t-conrey.c
index 9b39f5c5..5e5a060b 100644
--- a/acb_dirichlet/test/t-conrey.c
+++ b/acb_dirichlet/test/t-conrey.c
@@ -123,11 +123,11 @@ int main()
 
             if (!acb_dirichlet_conrey_eq(G, x, y))
             {
-                flint_printf("FAIL: conrey log and exp\n\n");
+                flint_printf("FAIL: conrey exp and log\n\n");
                 flint_printf("q = %wu\n\n", q);
                 flint_printf("conrey = ");
                 acb_dirichlet_conrey_print(G, x);
-                flint_printf("m = %wu\n\n", m);
+                flint_printf("\n\nm = %wu\n\n", m);
                 flint_printf("log = ");
                 acb_dirichlet_conrey_print(G, y);
                 flint_printf("\n\nnumber = %wu\n\n", y->n);
diff --git a/dlog.h b/dlog.h
index f62ef63a..b9352e26 100644
--- a/dlog.h
+++ b/dlog.h
@@ -235,11 +235,12 @@ ulong dlog_table(const dlog_table_t t, ulong b);
 ulong dlog_crt(const dlog_crt_t t, ulong b);
 ulong dlog_power(const dlog_power_t t, ulong b);
 ulong dlog_modpe(const dlog_modpe_t t, ulong b);
-ulong dlog_mod2e(const dlog_modpe_t t, ulong b);
 ulong dlog_bsgs(const dlog_bsgs_t t, ulong b);
 ulong dlog_rho(const dlog_rho_t t, ulong b);
-ulong dlog_1modpe_mod1p(ulong b1, ulong p, ulong e, ulong inv1p, nmod_t pe);
+ulong dlog_1modpe_1modp(ulong b1, ulong p, ulong e, ulong inv1p, nmod_t pe);
 ulong dlog_1modpe(const dlog_1modpe_t t, ulong b1, ulong p, ulong e, nmod_t pe);
+ulong dlog_mod2e_1mod4(ulong b1, ulong e, ulong inva, nmod_t pe);
+ulong dlog_mod2e(const dlog_modpe_t t, ulong b);
 /*#define dlog_bsgs(t, b) n_discrete_log_bsgs_table(t, b)*/
 
 #define DLOG_SMALL_LIM 50
diff --git a/dlog/1modpe.c b/dlog/1modpe.c
index a9d12817..ecfa98c3 100644
--- a/dlog/1modpe.c
+++ b/dlog/1modpe.c
@@ -19,7 +19,7 @@ dlog_1modpe(const dlog_1modpe_t t, ulong b1, ulong p, ulong e, nmod_t pe)
     else
     {
         ulong logb1;
-        logb1 = dlog_1modpe_mod1p(b1, p, e, t->inv1p, pe);
+        logb1 = dlog_1modpe_1modp(b1, p, e, t->inv1p, pe);
         /* only need mod p^(e-1) */
         return nmod_mul(logb1, t->invloga1, pe);
     }
diff --git a/dlog/1modpe_init.c b/dlog/1modpe_init.c
index c8bef0b1..a28323bc 100644
--- a/dlog/1modpe_init.c
+++ b/dlog/1modpe_init.c
@@ -25,7 +25,7 @@ dlog_1modpe_init(dlog_1modpe_t t, ulong a1, ulong p, ulong e, nmod_t pe)
         if (a1 == 1)
             abort();
         t->inv1p = nmod_inv(1 + p, pe); /* 1 - p + p^2 - ... */
-        loga1 = dlog_1modpe_mod1p(a1, p, e, t->inv1p, pe);
+        loga1 = dlog_1modpe_1modp(a1, p, e, t->inv1p, pe);
         /* only need inverse mod p^(e-1) but does not hurt */
         t->invloga1 = nmod_inv(loga1, pe);
     }
diff --git a/dlog/1modpe_mod1p.c b/dlog/1modpe_mod1p.c
index 830e1717..9693769f 100644
--- a/dlog/1modpe_mod1p.c
+++ b/dlog/1modpe_mod1p.c
@@ -13,7 +13,7 @@
 
 /* for odd prime p, assume b1 = 1 mod p */
 ulong
-dlog_1modpe_mod1p(ulong b1, ulong p, ulong e, ulong inv1p, nmod_t pe)
+dlog_1modpe_1modp(ulong b1, ulong p, ulong e, ulong inv1p, nmod_t pe)
 {
     int f;
     ulong x, xf, pf, pf1;
diff --git a/dlog/mod2e.c b/dlog/mod2e.c
index ed051503..2ef8e655 100644
--- a/dlog/mod2e.c
+++ b/dlog/mod2e.c
@@ -11,33 +11,37 @@
 
 #include "dlog.h"
 
+ulong
+dlog_mod2e_1mod4(ulong b1, ulong e, ulong inv5, nmod_t pe)
+{
+    slong f;
+    ulong pf1, pf, x, xf;
+    pf1 = 1;
+    pf = 4;
+    x = 0;
+    for (f = 2; f < e; f++)
+    {
+        if (b1 % pf != 1)
+        {
+            flint_printf("ERROR dlog_mod2e: %wu %% %wu != 1 mod %wu\n\n",
+                    b1, pf, pe.n);
+            abort();
+        }
+        xf = (b1 - 1) / pf;
+        xf = (f == 2) ? xf % 4 : (xf % 2) * (pf1 / 2);
+        b1 = nmod_mul(b1, nmod_pow_ui(inv5, xf, pe), pe);
+        x += xf;
+        pf1 = pf;
+        pf *= 2;
+    }
+    return x;
+}
+
 ulong
 dlog_mod2e(const dlog_modpe_t t, ulong b1)
 {
     if (t->e == 2)
         return (b1 % 4) == 3;
     else
-    {
-        slong f;
-        ulong pf1, pf, x, xf;
-        pf1 = 1;
-        pf = 4;
-        x = 0;
-        for (f = 2; f < t->e; f++)
-        {
-            if (b1 % pf != 1)
-            {
-                flint_printf("ERROR dlog_mod2e: %wu %% %wu != 1 mod %wu\n\n",
-                        b1, pf, t->pe.n);
-                abort();
-            }
-            xf = (b1 - 1) / pf;
-            xf = (f == 2) ? xf % 4 : (xf % 2) * (pf1 / 2);
-            b1 = nmod_mul(b1, nmod_pow_ui(t->inva, xf, t->pe), t->pe);
-            x += xf;
-            pf1 = pf;
-            pf *= 2;
-        }
-        return x;
-    }
+        return dlog_mod2e_1mod4(b1, t->e, t->inva, t->pe);
 }