diff --git a/as_covers/as_cover_class.sage b/as_covers/as_cover_class.sage
index 5c28ba0..4b2ed95 100644
--- a/as_covers/as_cover_class.sage
+++ b/as_covers/as_cover_class.sage
@@ -303,7 +303,7 @@ class as_cover:
         p = self.characteristic
         n = self.height
         F = self.base_ring
-        rr_space = self.at_most_poles(threshold)
+        rr_space = self.at_most_poles(threshold, threshold=int(sqrt(threshold))) #there are two thresholds, how to pick them? we picked sqrt randomly
         list_of_fcts = [ff for ff in rr_space if ff.valuation(place)%p != 0]
         list_of_fcts2 = [len(str(ff)) for ff in list_of_fcts]
         i_min = list_of_fcts2.index(min(list_of_fcts2))
@@ -337,7 +337,7 @@ class as_cover:
     
     def fiber(self, place = 0):
         'Gives representatives for the quotient G/G_P for given place. Those are in bijection with the fiber.'
-        result = [AS.group.one]
+        result = [self.group.one]
         p = self.characteristic
         G = self.group
         H = self.stabilizer(place = place)
diff --git a/as_covers/template.sage b/as_covers/template.sage
index 3a2fc2e..dbd2c4d 100644
--- a/as_covers/template.sage
+++ b/as_covers/template.sage
@@ -196,7 +196,7 @@ def hypoelementary_template(p, m, b, zeta):
     x = R.gens()[-2]
     y = R.gens()[-1]
     group = hypoelementary(p, m, b)
-    fcts = [1/(zeta - b)*f[0]^p*z[0]^p - 1/(zeta - b)*f[0]*z[0]
+    fcts = [1/(zeta - b)*f[0]^p*z[0]^p - 1/(zeta - b)*f[0]*z[0]]
     gp_action = []
     gp_action += [b*z[0]+f[0]*y, x, zeta*y]
     gp_action += [z[0]+1, x, y]
diff --git a/drafty/draft2.sage b/drafty/draft2.sage
index e3f61fa..1895f65 100644
--- a/drafty/draft2.sage
+++ b/drafty/draft2.sage
@@ -1,13 +1,6 @@
 p = 3
 F = GF(3)
-#F.<a> = GF(3^2)
-Rx.<x> = PolynomialRing(F)
-P1 = superelliptic(x^2 + 1, 2)
-fct1 = (P1.x)^2
-fct2 = (fct1 + P1.one/(P1.y - P1.x))
-fct3 = 0*P1.x
-C = heisenberg_cover(P1, [fct1, fct2, fct3], prec=200)
-print(C, '\n', C.genus(), '\n', C.jumps)
-#B = C.holomorphic_differentials_basis()
-#print("Computed basis")
-#a1, b1, c1 = heisenberg_group_action_matrices_holo(C, basis = B)
\ No newline at end of file
+R.<x> = PolynomialRing(GF(p))
+P1 = superelliptic(x, 1)
+AS = witt_cover([P1.x^5, P1.x^1, P1.x^1], prec=1000)
+AS1 = witt_cover([P1.x^5, P1.x^1], prec=400)
\ No newline at end of file