The NumberField containing both embeddings should be larger. The morphisms 
also clearly show that something is going wrong:

sage: nf = NumberField(x^8 - 3*x^7 + 61/3*x^6 - 9*x^5 + 298*x^4 + 458*x^3 + 
1875*x^2 + 4293*x + 3099, 'z', embedding=-1.18126721294295 + 
3.02858651117832j)
sage: nf2 = NumberField(x^8 - 3*x^7 + 61/3*x^6 - 9*x^5 + 298*x^4 + 458*x^3 
+ 1875*x^2 + 4293*x + 3099, 'z', embedding=-1.18126721294295 - 
3.02858651117832j) 
sage: nf.composite_fields(nf2,both_maps = True) 
[(Number Field in z with defining polynomial x^8 - 3*x^7 + 61/3*x^6 - 9*x^5 
+ 298*x^4 + 458*x^3 + 1875*x^2 + 4293*x + 3099, 
Ring endomorphism of Number Field in z with defining polynomial x^8 - 3*x^7 
+ 61/3*x^6 - 9*x^5 + 298*x^4 + 458*x^3 + 1875*x^2 + 4293*x + 3099 
Defn: z |--> z, 
Ring morphism: 
From: Number Field in z with defining polynomial x^8 - 3*x^7 + 61/3*x^6 - 
9*x^5 + 298*x^4 + 458*x^3 + 1875*x^2 + 4293*x + 3099 
To: Number Field in z with defining polynomial x^8 - 3*x^7 + 61/3*x^6 - 
9*x^5 + 298*x^4 + 458*x^3 + 1875*x^2 + 4293*x + 3099 
Defn: z |--> z, 
 +Infinity)]

I couldn't find a bug on trac for it. I think there should be one filed.

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