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The issue is that the Dirichlet coefficients and the Euler polynomials are both swapped in the database.
I wrote a patch #4887 many years ago to fix the Euler factors, but looks like I forgot about the Dirichlet coefficients.
From the feedback page:
On
https://www.lmfdb.org/L/1/2e2/4.3/r1/0/0
It seems like when the Euler factors should be 1 - T, it is listed as 1 + T, and vice versa.
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