Let $E:y^2＝x^3-x/ \Bbb{Q}(i)$ be elliptic curve and $L(E,1)$ be a special value of $L$ function of $E$ at $1$.

Let $L(ψ,1)$ be value at $1$ of Hecke $L$ function with respect to Hecke character $ψ$, It is known that $L(E,1)＝L( \bar{ψ},1)L(ψ,1)$.

In this case, why $L(ψ,1)＝1$ ?

I may forget some trivial fact about Hecke $L$ character. Thank you for your help.

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