Working Jacobi symbol function!

lucas.py

@@ -43,23 +43,34 @@ def Legendere(a, p):
 def Jacobi(a, n):
     if (n % 2 == 0):
         raise ValueError("n must be odd, is {}".format(n))
-    a = a % n
-    mv = 1
-    while a != 0 and a % 2 == 0:
-        a = a / 2
+    if a % n != a:
+        return Jacobi(a%n, n)
+    if a != 0 and a % 2 == 0:
         nm8 = n % 8
         if (nm8 == 3 or nm8 == 5):
-            mv = mv * -1
+            return -1 * Jacobi(a//2, n)
+        else:
+            return Jacobi(a//2, n)
     if a == 1:
-        return mv * 1
+        return 1
     if gcd(a, n) != 1:
         return 0
     if a == 0 and n == 1:
-        return mv * 1
-    return mv * Jacobi(n, a)
+        return 1
+    if n % 4 == 3 and a % 4 == 3:
+        return -1 * Jacobi(n, a)
+    return Jacobi(n, a)
+
+print("   ", end=" ")
+for k in range(1, 10):
+    print("{}".format(k).rjust(2, " "), end=" ")
+print()
 
 for n in range(1, 21, 2):
-    print("{}:\t{}".format(n, Jacobi(3, n)))
+    print("{}:".format(n).rjust(3, " "), end=" ")
+    for k in range(1, 10):
+        print("{}".format(Jacobi(k, n)).rjust(2, " "), end=" ")
+    print()