Geodesic
The Parity Distribution of Traces in Imaginary Quadratic Fields
Canadian mathematical bulletin, Tome 34 (1991) no. 2, pp. 196-201

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Computations of the Iwasawa λ -invariant for imaginary quadratic fields showed a discrepancy in the proportion of even and odd traces of certain integers from these imaginary quadratic fields. This paper shows that such a discrepancy is in some sense to be expected and that the proportion of even and odd traces of principal generators of powers of prime ideals in imaginary quadratic fields is related to the 3-primary component of the class group. 
Dummit, D. S. The Parity Distribution of Traces in Imaginary Quadratic Fields. Canadian mathematical bulletin, Tome 34 (1991) no. 2, pp. 196-201. doi: 10.4153/CMB-1991-031-2
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     title = {The {Parity} {Distribution} of {Traces} in {Imaginary} {Quadratic} {Fields}},
     journal = {Canadian mathematical bulletin},
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     doi = {10.4153/CMB-1991-031-2},
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