def twist_zeros(self, n, dmin, dmax):
r"""
Return first $n$ real parts of nontrivial zeros of
$L(E,s,\chi_d)$ for each quadratic character $\chi_d$ with
$d_{\min} \leq d \leq d_{\max}$.
\note{The L-series is normalized so that the center of the
critical strip is 1.}
INPUT:
n -- integer
dmin -- integer
dmax -- integer
OUTPUT:
dict -- keys are the discriminants $d$, and
values are list of corresponding zeros.
EXAMPLES::
sage: E = EllipticCurve('37a')
sage: E.lseries().twist_zeros(3, -4, -3) # long time
{-4: [1.60813783, 2.96144840, 3.89751747], -3: [2.06170900, 3.48216881, 4.45853219]}
"""
from sage.lfunctions.lcalc import lcalc
return lcalc.twist_zeros(n, dmin, dmax, L=self.__E)
def twist_zeros(self, n, dmin, dmax):
r"""
Return first `n` real parts of nontrivial zeros of
`L(E,s,\chi_d)` for each quadratic character `\chi_d` with
`d_{\min} \leq d \leq d_{\max}`.
.. note::
The L-series is normalized so that the center of the
critical strip is 1.
INPUT:
- ``n`` -- integer
- ``dmin`` -- integer
- ``dmax`` -- integer
OUTPUT:
- dict -- keys are the discriminants `d`, and
values are list of corresponding zeros.
EXAMPLES::
sage: E = EllipticCurve('37a')
sage: E.lseries().twist_zeros(3, -4, -3) # long time
{-4: [1.60813783, 2.96144840, 3.89751747], -3: [2.06170900, 3.48216881, 4.45853219]}
"""
from sage.lfunctions.lcalc import lcalc
return lcalc.twist_zeros(n, dmin, dmax, L=self.__E)
def twist_zeros(self, n, dmin, dmax):
r"""
Return first $n$ real parts of nontrivial zeros of
$L(E,s,\chi_d)$ for each quadratic character $\chi_d$ with
$d_{\min} \leq d \leq d_{\max}$.
\note{The L-series is normalized so that the center of the
critical strip is 1.}
INPUT:
n -- integer
dmin -- integer
dmax -- integer
OUTPUT:
dict -- keys are the discriminants $d$, and
values are list of corresponding zeros.
EXAMPLES::
sage: E = EllipticCurve('37a')
sage: E.lseries().twist_zeros(3, -4, -3) # long time
*** Warning:...new stack size = ...
{-4: [1.60813783, 2.96144840, 3.89751747], -3: [2.06170900, 3.48216881, 4.45853219]}
"""
from sage.lfunctions.lcalc import lcalc
return lcalc.twist_zeros(n, dmin, dmax, L=self.__E)
