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Here is way to do it.

sage: F.<z> = CyclotomicField(7)
sage: def Frob(p):                                                                             
    return F.hom([z^p])
....: 
sage: Frob(2)
Ring endomorphism of Cyclotomic Field of order 7 and degree 6
  Defn: z |--> z^2
sage: Frob(3)                                                                                            
Ring endomorphism of Cyclotomic Field of order 7 and degree 6
  Defn: z |--> z^3
sage: Frob(5)                                                                                            
Ring endomorphism of Cyclotomic Field of order 7 and degree 6
  Defn: z |--> z^5
sage: Frob(97)                                                                                           
Ring endomorphism of Cyclotomic Field of order 7 and degree 6
  Defn: z |--> -z^5 - z^4 - z^3 - z^2 - z - 1
 

Here is way to do it.

 sage: F.<z> = CyclotomicField(7)
sage: def Frob(p):                                                  return F.hom([z^p])
....: 
sage: Frob(2)
Ring endomorphism of Cyclotomic Field of order 7 and degree 6
 Defn: z |--> z^2
sage: Frob(3)                                                                                            
Ring endomorphism of Cyclotomic Field of order 7 and degree 6
     sage:Frob(3)                                                                                            
Ring endomorphism of Cyclotomic Field of order 7 and degree 6
Defn: z |--> z^3
sage: Frob(5)                                                                                            

sage:Frob(5)
Ring endomorphism of Cyclotomic Field of order 7 and degree 6 Defn: z |--> z^5 sage: sage: Frob(97)
Ring endomorphism of Cyclotomic Field of order 7 and degree 6 Defn: z |--> -z^5 - z^4 - z^3 - z^2 - z - 1

1

Here is way to do it.

sage: F.<z> = CyclotomicField(7)
sage: def Frob(p):                                                
return F.hom([z^p])
....: 
sage: Frob(2)
Ring endomorphism of Cyclotomic Field of order 7 and degree 6
Defn: z |--> z^2
 sage:Frob(3)                                                                                            
Ring endomorphism of Cyclotomic Field of order 7 and degree 6
Defn: z |--> z^3

sage:Frob(5)
Ring endomorphism of Cyclotomic Field of order 7 and degree 6

Defn: z |--> z^5 sage: Frob(97)
Ring endomorphism of Cyclotomic Field of order 7 and degree 6 Defn: z |--> -z^5 - z^4 - z^3 - z^2 - z - 1

Here is way to do it.

sage: F.<z> = CyclotomicField(7)
sage: def Frob(p):                                                
return F.hom([z^p])
....: 
sage: Frob(2)
Ring endomorphism of Cyclotomic Field of order 7 and degree 6
Defn: z |--> z^2
sage:Frob(3)                                                                                            
Ring endomorphism of Cyclotomic Field of order 7 and degree 6
Defn: z |--> z^3
sage:Frob(5)                                                                                            
Ring endomorphism of Cyclotomic Field of order 7 and degree 6

Defn: z |--> z^5 sage: Frob(97)
Ring endomorphism of Cyclotomic Field of order 7 and degree 6 Defn: z |--> -z^5 - z^4 - z^3 - z^2 - z - 1

Here is way to do it.

sage: F.<z> = CyclotomicField(7)
sage: def Frob(p):                                                  return F.hom([z^p])
....: 
sage: Frob(2)
Ring endomorphism of Cyclotomic Field of order 7 and degree 6
 Defn: z |--> z^2
sage:Frob(3) sage: Frob(3)                                                                                            
Ring endomorphism of Cyclotomic Field of order 7 and degree 6
 Defn: z |--> z^3
sage:Frob(5) sage: Frob(5)                                                                                            
Ring endomorphism of Cyclotomic Field of order 7 and degree 6
 Defn: z |--> z^5
sage:  Frob(97)     
Ring endomorphism of Cyclotomic Field of order 7 and degree 6
 Defn: z |--> -z^5 - z^4 - z^3 - z^2 - z - 1