dokchitser Lseries at least for number fields claims a pole at zero, though the zeta function has a zero there
sage: K.<a> = NumberField(x^22)
sage: z = K.zeta_function()
sage: z(0)
Traceback (most recent call last):
...
ArithmeticError: ### user error: L*(s) has a pole at s=0
sage: z(0.0000001)
4.40686861437826e8
Notice that there is in fact a zero at s=0, not a pole as the ArithmeticError? claims.
In fact, it's a theorem that there is a zero at s=0 of order the unit rank of the number field.
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The function
L*(s) = sqrt(8)^s/pi^s * gamma(s/2)^2
does have a pole at s=0, even though L(s) doesn't. That being said, it shouldn't raise this error.I have made some progress on the reimplementation of dokchitser the last couple of days.