Sample 1.  Real root of f(x) = x**5 - 3x**4 + x**3 - 4x**2 + x - 6 = 0.


 Iteration       Newton Approximation

         0       3.120000000000000000000000000000000000000000000000000000000000

         1       3.120656718532108533919391265947916793506741449899073468862023

         2       3.120656215327022122238354686569835883519704471397219749798884

         3       3.120656215326726500470956115551705969611230193197937042123082

         4       3.120656215326726500470956013523797484654623935599078168006617

         5       3.120656215326726500470956013523797484654623935599066014988828

         6       3.120656215326726500470956013523797484654623935599066014988828



 Sample 2.          109 terms were added

 Zeta(3) =    1.202056903159594285399738161511449990764986292340498881792272



 Sample 3.           22 values were tested

 p =   1000000000000000000000000000000000000000000000000000000000000000659661


 Sample 4.  Complex root of f(x) = x**5 - 3x**4 + x**3 - 4x**2 + x - 6 = 0.


 Iteration       Newton Approximation

     0     .560000000000000000000000000000 + 1.060000000000000000000000000000 i

     1     .561964780980333719745880263787 + 1.061135231152741154895778904059 i

     2     .561958308372772219534516409947 + 1.061134679566247415769456345141 i

     3     .561958308335403235495113920123 + 1.061134679604332556981397796290 i

     4     .561958308335403235498111195347 + 1.061134679604332556983391239059 i

     5     .561958308335403235498111195347 + 1.061134679604332556983391239059 i



 Sample 5.           44 terms were added to get Exp(1.23-2.34i)

 Result= -2.379681796854777515745457977697 - 2.458032970832342652397461908326 i


 All results were ok.