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### Number field basis containing 1

In Sage, the default basis for a maximal order $O_K$ often does not contain the element $1$:

sage: QuadraticField(-3).ring_of_integers().basis()
[1/2*a + 1/2, a]


However, $1$ is always a primitive lattice vector in $O_K$. Is there an elegant way to produce a basis containing $1$?