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-rw-r--r--sagemath-lcalc2.patch507
1 files changed, 507 insertions, 0 deletions
diff --git a/sagemath-lcalc2.patch b/sagemath-lcalc2.patch
new file mode 100644
index 000000000000..77e58512909e
--- /dev/null
+++ b/sagemath-lcalc2.patch
@@ -0,0 +1,507 @@
+diff --git a/src/sage/lfunctions/lcalc.py b/src/sage/lfunctions/lcalc.py
+index aabbd47..6efa5fe 100644
+--- a/src/sage/lfunctions/lcalc.py
++++ b/src/sage/lfunctions/lcalc.py
+@@ -225,19 +225,54 @@ class LCalc(SageObject):
+ EXAMPLES::
+
+ sage: I = CC.0
+- sage: lcalc.values_along_line(0.5, 0.5+20*I, 5)
+- [(0.500000000, -1.46035451), (0.500000000 + 4.00000000*I, 0.606783764 + 0.0911121400*I), (0.500000000 + 8.00000000*I, 1.24161511 + 0.360047588*I), (0.500000000 + 12.0000000*I, 1.01593665 - 0.745112472*I), (0.500000000 + 16.0000000*I, 0.938545408 + 1.21658782*I)]
++ sage: values = lcalc.values_along_line(0.5, 0.5+20*I, 5)
++ sage: values[0][0] # abs tol 1e-8
++ 0.5
++ sage: values[0][1] # abs tol 1e-8
++ -1.46035451 + 0.0*I
++ sage: values[1][0] # abs tol 1e-8
++ 0.5 + 4.0*I
++ sage: values[1][1] # abs tol 1e-8
++ 0.606783764 + 0.0911121400*I
++ sage: values[2][0] # abs tol 1e-8
++ 0.5 + 8.0*I
++ sage: values[2][1] # abs tol 1e-8
++ 1.24161511 + 0.360047588*I
++ sage: values[3][0] # abs tol 1e-8
++ 0.5 + 12.0*I
++ sage: values[3][1] # abs tol 1e-8
++ 1.01593665 - 0.745112472*I
++ sage: values[4][0] # abs tol 1e-8
++ 0.5 + 16.0*I
++ sage: values[4][1] # abs tol 1e-8
++ 0.938545408 + 1.21658782*I
+
+ Sometimes warnings are printed (by lcalc) when this command is
+ run::
+
+ sage: E = EllipticCurve('389a')
+- sage: E.lseries().values_along_line(0.5, 3, 5)
+- [(0.000000000, 0.209951303),
+- (0.500000000, -...e-16),
+- (1.00000000, 0.133768433),
+- (1.50000000, 0.360092864),
+- (2.00000000, 0.552975867)]
++ sage: values = E.lseries().values_along_line(0.5, 3, 5)
++ sage: values[0][0] # abs tol 1e-8
++ 0.0
++ sage: values[0][1] # abs tol 1e-8
++ 0.209951303 + 0.0*I
++ sage: values[1][0] # abs tol 1e-8
++ 0.5
++ sage: values[1][1] # abs tol 1e-8
++ 0.0 + 0.0*I
++ sage: values[2][0] # abs tol 1e-8
++ 1.0
++ sage: values[2][1] # abs tol 1e-8
++ 0.133768433 - 0.0*I
++ sage: values[3][0] # abs tol 1e-8
++ 1.5
++ sage: values[3][1] # abs tol 1e-8
++ 0.360092864 - 0.0*I
++ sage: values[4][0] # abs tol 1e-8
++ 2.0
++ sage: values[4][1] # abs tol 1e-8
++ 0.552975867 + 0.0*I
++
+ """
+ L = self._compute_L(L)
+ CC = sage.rings.all.ComplexField(prec)
+@@ -281,8 +316,31 @@ class LCalc(SageObject):
+
+ EXAMPLES::
+
+- sage: lcalc.twist_values(0.5, -10, 10)
+- [(-8, 1.10042141), (-7, 1.14658567), (-4, 0.667691457), (-3, 0.480867558), (5, 0.231750947), (8, 0.373691713)]
++ sage: values = lcalc.twist_values(0.5, -10, 10)
++ sage: values[0][0]
++ -8
++ sage: values[0][1] # abs tol 1e-8
++ 1.10042141 + 0.0*I
++ sage: values[1][0]
++ -7
++ sage: values[1][1] # abs tol 1e-8
++ 1.14658567 + 0.0*I
++ sage: values[2][0]
++ -4
++ sage: values[2][1] # abs tol 1e-8
++ 0.667691457 + 0.0*I
++ sage: values[3][0]
++ -3
++ sage: values[3][1] # abs tol 1e-8
++ 0.480867558 + 0.0*I
++ sage: values[4][0]
++ 5
++ sage: values[4][1] # abs tol 1e-8
++ 0.231750947 + 0.0*I
++ sage: values[5][0]
++ 8
++ sage: values[5][1] # abs tol 1e-8
++ 0.373691713 + 0.0*I
+ """
+ L = self._compute_L(L)
+ CC = sage.rings.all.ComplexField(prec)
+diff --git a/src/sage/lfunctions/zero_sums.pyx b/src/sage/lfunctions/zero_sums.pyx
+index 225fe7d..8b0e566 100644
+--- a/src/sage/lfunctions/zero_sums.pyx
++++ b/src/sage/lfunctions/zero_sums.pyx
+@@ -829,8 +829,11 @@ cdef class LFunctionZeroSum_abstract(SageObject):
+ EXAMPLES::
+
+ sage: E = EllipticCurve("11a")
+- sage: E.lseries().zeros(2)
+- [6.36261389, 8.60353962]
++ sage: zeros = E.lseries().zeros(2)
++ sage: zeros[0] # abs tol 1e-8
++ 6.36261389
++ sage: zeros[1] # abs tol 1e-8
++ 8.60353962
+
+ E is a rank zero curve; the lowest zero has imaginary part ~6.36. The
+ zero sum with tau=0 indicates that there are no zeros at the central
+diff --git a/src/sage/libs/lcalc/lcalc_Lfunction.pxd b/src/sage/libs/lcalc/lcalc_Lfunction.pxd
+index d1dbb5d..5edf084 100644
+--- a/src/sage/libs/lcalc/lcalc_Lfunction.pxd
++++ b/src/sage/libs/lcalc/lcalc_Lfunction.pxd
+@@ -21,7 +21,7 @@ cdef extern from "lcalc_sage.h":
+ int (* compute_rank) ()
+ double (* N) (double T)
+ void (* find_zeros_v)(double T1, double T2, double stepsize, doublevec result )
+- void (*find_zeros_via_N_v)(long count,int do_negative,double max_refine, int rank, int test_explicit_formula, doublevec result)
++ int (*find_zeros)(long count, long start, double max_refine, int rank, const char* message_stamp, doublevec* result)
+ void (*print_data_L)()
+
+ #Constructor and destructor
+@@ -38,7 +38,7 @@ cdef extern from "lcalc_sage.h":
+ double (* N) (double T)
+ double *dirichlet_coefficient
+ void (* find_zeros_v)(double T1, double T2, double stepsize, doublevec result )
+- void (*find_zeros_via_N_v)(long count,int do_negative,double max_refine, int rank, int test_explicit_formula, doublevec result)
++ int (*find_zeros)(long count, long start, double max_refine, int rank, const char* message_stamp, doublevec* result)
+ void (*print_data_L)()
+
+ #Constructor and destructor
+@@ -54,7 +54,7 @@ cdef extern from "lcalc_sage.h":
+ int (* compute_rank) ()
+ double (* N) (double T)
+ void (* find_zeros_v)(double T1, double T2, double stepsize, doublevec result )
+- void (*find_zeros_via_N_v)(long count,int do_negative,double max_refine, int rank, int test_explicit_formula, doublevec result)
++ int (*find_zeros)(long count, long start, double max_refine, int rank, const char* message_stamp, doublevec* result)
+ void (*print_data_L)()
+
+ #Constructor and destructor
+@@ -70,7 +70,7 @@ cdef extern from "lcalc_sage.h":
+ int (* compute_rank) ()
+ double (* N) (double T)
+ void (* find_zeros_v)(double T1, double T2, double stepsize, doublevec result )
+- void (*find_zeros_via_N_v)(long count,int do_negative,double max_refine, int rank, int test_explicit_formula, doublevec result)#puts result in vector<double> result
++ int (*find_zeros)(long count, long start, double max_refine, int rank, const char* message_stamp, doublevec* result)
+ void (*find_zeros_via_N)(long count,int do_negative,double max_refine, int rank, int test_explicit_formula, char *filename) #puts result in filename
+
+ #Constructor and destructor
+@@ -111,7 +111,7 @@ cdef class Lfunction:
+ #strange bug, replacing Double with double gives me a compile error
+ cdef Double __typedN(self, double T)
+ cdef void __find_zeros_v(self, double T1, double T2, double stepsize,doublevec *result)
+- cdef void __find_zeros_via_N_v(self, long count,int do_negative,double max_refine, int rank, int test_explicit_formula,doublevec *result)
++ cdef int __find_zeros(self, long count, long start, double max_refine, int rank, const char* message_stamp, doublevec* result)
+
+ cdef str _repr
+
+diff --git a/src/sage/libs/lcalc/lcalc_Lfunction.pyx b/src/sage/libs/lcalc/lcalc_Lfunction.pyx
+index 7e54d7e..88a6e13 100644
+--- a/src/sage/libs/lcalc/lcalc_Lfunction.pyx
++++ b/src/sage/libs/lcalc/lcalc_Lfunction.pyx
+@@ -143,29 +143,29 @@ cdef class Lfunction:
+ sage: chi = DirichletGroup(5)[2] #This is a quadratic character
+ sage: from sage.libs.lcalc.lcalc_Lfunction import *
+ sage: L=Lfunction_from_character(chi, type="int")
+- sage: L.value(.5) # abs tol 3e-15
++ sage: L.value(.5) # abs tol 1e-8
+ 0.231750947504016 + 5.75329642226136e-18*I
+- sage: L.value(.2+.4*I)
+- 0.102558603193... + 0.190840777924...*I
++ sage: L.value(.2+.4*I) # abs tol 1e-8
++ 0.102558603193 + 0.190840777924*I
+
+ sage: L=Lfunction_from_character(chi, type="double")
+- sage: L.value(.6) # abs tol 3e-15
++ sage: L.value(.6) # abs tol 1e-8
+ 0.274633355856345 + 6.59869267328199e-18*I
+- sage: L.value(.6+I)
+- 0.362258705721... + 0.433888250620...*I
++ sage: L.value(.6+I) # abs tol 1e-8
++ 0.362258705721 + 0.433888250620*I
+
+ sage: chi = DirichletGroup(5)[1]
+ sage: L=Lfunction_from_character(chi, type="complex")
+- sage: L.value(.5)
+- 0.763747880117... + 0.216964767518...*I
+- sage: L.value(.6+5*I)
+- 0.702723260619... - 1.10178575243...*I
++ sage: L.value(.5) # abs tol 1e-8
++ 0.763747880117 + 0.216964767518*I
++ sage: L.value(.6+5*I) # abs tol 1e-8
++ 0.702723260619 - 1.10178575243*I
+
+ sage: L=Lfunction_Zeta()
+- sage: L.value(.5)
+- -1.46035450880...
+- sage: L.value(.4+.5*I)
+- -0.450728958517... - 0.780511403019...*I
++ sage: L.value(.5) # abs tol 1e-8
++ -1.46035450880 + 0.0*I
++ sage: L.value(.4+.5*I) # abs tol 1e-8
++ -0.450728958517 - 0.780511403019*I
+ """
+ cdef ComplexNumber complexified_s = CCC(s)
+ cdef c_Complex z = new_Complex(mpfr_get_d(complexified_s.__re, MPFR_RNDN), mpfr_get_d(complexified_s.__im, MPFR_RNDN))
+@@ -185,23 +185,21 @@ cdef class Lfunction:
+ sage: chi = DirichletGroup(5)[2] # Quadratic character
+ sage: from sage.libs.lcalc.lcalc_Lfunction import *
+ sage: L = Lfunction_from_character(chi, type="int")
+- sage: L.hardy_z_function(0)
+- 0.231750947504...
+- sage: L.hardy_z_function(.5).imag() # abs tol 1e-15
++ sage: L.hardy_z_function(0) # abs tol 1e-8
++ 0.231750947504 + 0.0*I
++ sage: L.hardy_z_function(.5).imag() # abs tol 1e-8
+ 1.17253174178320e-17
+- sage: L.hardy_z_function(.4+.3*I)
+- 0.2166144222685... - 0.00408187127850...*I
+ sage: chi = DirichletGroup(5)[1]
+ sage: L = Lfunction_from_character(chi, type="complex")
+- sage: L.hardy_z_function(0)
+- 0.793967590477...
+- sage: L.hardy_z_function(.5).imag() # abs tol 1e-15
++ sage: L.hardy_z_function(0) # abs tol 1e-8
++ 0.793967590477 + 0.0*I
++ sage: L.hardy_z_function(.5).imag() # abs tol 1e-8
+ 0.000000000000000
+ sage: E = EllipticCurve([-82,0])
+ sage: L = Lfunction_from_elliptic_curve(E, number_of_coeffs=40000)
+- sage: L.hardy_z_function(2.1)
+- -0.00643179176869...
+- sage: L.hardy_z_function(2.1).imag() # abs tol 1e-15
++ sage: L.hardy_z_function(2.1) # abs tol 1e-8
++ -0.00643179176863296 - 1.47189978221606e-19*I
++ sage: L.hardy_z_function(2.1).imag() # abs tol 1e-8
+ -3.93833660115668e-19
+ """
+ #This takes s -> .5 + I*s
+@@ -241,8 +239,8 @@ cdef class Lfunction:
+ sage: from sage.libs.lcalc.lcalc_Lfunction import *
+ sage: chi = DirichletGroup(5)[2] #This is a quadratic character
+ sage: L=Lfunction_from_character(chi, type="complex")
+- sage: L.__N(10)
+- 3.17043978326...
++ sage: L.__N(10) # abs tol 1e-8
++ 4.0
+ """
+ cdef RealNumber real_T=RRR(T)
+ cdef double double_T = mpfr_get_d(real_T.value, MPFR_RNDN)
+@@ -307,18 +305,21 @@ cdef class Lfunction:
+ return returnvalue
+
+ #The default values are from L.h. See L.h
+- def find_zeros_via_N(self, count=0, do_negative=False, max_refine=1025,
+- rank=-1, test_explicit_formula=0):
++ def find_zeros_via_N(self, count=0, start=0, max_refine=1025, rank=-1):
+ """
+- Finds ``count`` number of zeros with positive imaginary part
+- starting at real axis. This function also verifies that all
+- the zeros have been found.
++ Find ``count`` zeros (in order of increasing magnitude) and output
++ their imaginary parts. This function verifies that no zeros
++ are missed, and that all values output are indeed zeros.
++
++ If this L-function is self-dual (if its Dirichlet coefficients
++ are real, up to a tolerance of 1e-6), then only the zeros with
++ positive imaginary parts are output. Their conjugates, which
++ are also zeros, are not output.
+
+ INPUT:
+
+ - ``count`` - number of zeros to be found
+- - ``do_negative`` - (default: False) False to ignore zeros below the
+- real axis.
++ - ``start`` - (default: 0) how many initial zeros to skip
+ - ``max_refine`` - when some zeros are found to be missing, the step
+ size used to find zeros is refined. max_refine gives an upper limit
+ on when lcalc should give up. Use default value unless you know
+@@ -326,13 +327,9 @@ cdef class Lfunction:
+ - ``rank`` - integer (default: -1) analytic rank of the L-function.
+ If -1 is passed, then we attempt to compute it. (Use default if in
+ doubt)
+- - ``test_explicit_formula`` - integer (default: 0) If nonzero, test
+- the explicit formula for additional confidence that all the zeros
+- have been found and are accurate. This is still being tested, so
+- using the default is recommended.
+
+ OUTPUT:
+-
++
+ list -- A list of the imaginary parts of the zeros that have been found
+
+ EXAMPLES::
+@@ -349,21 +346,26 @@ cdef class Lfunction:
+
+ sage: chi = DirichletGroup(5)[1]
+ sage: L=Lfunction_from_character(chi, type="complex")
+- sage: L.find_zeros_via_N(3)
+- [6.18357819545..., 8.45722917442..., 12.6749464170...]
++ sage: zeros = L.find_zeros_via_N(3)
++ sage: zeros[0] # abs tol 1e-8
++ -4.13290370521286
++ sage: zeros[1] # abs tol 1e-8
++ 6.18357819545086
++ sage: zeros[2] # abs tol 1e-8
++ 8.45722917442320
+
+ sage: L=Lfunction_Zeta()
+ sage: L.find_zeros_via_N(3)
+ [14.1347251417..., 21.0220396387..., 25.0108575801...]
+ """
+- cdef Integer count_I = Integer(count)
+- cdef Integer do_negative_I = Integer(do_negative)
+- cdef RealNumber max_refine_R = RRR(max_refine)
+- cdef Integer rank_I = Integer(rank)
+- cdef Integer test_explicit_I = Integer(test_explicit_formula)
++
++ # This is the default value for message_stamp, but we have to
++ # pass it explicitly since we're passing in the next argument,
++ # our &result pointer.
++ cdef const char* message_stamp = ""
+ cdef doublevec result
+ sig_on()
+- self.__find_zeros_via_N_v(mpz_get_si(count_I.value), mpz_get_si(do_negative_I.value), mpfr_get_d(max_refine_R.value, MPFR_RNDN), mpz_get_si(rank_I.value), mpz_get_si(test_explicit_I.value), &result)
++ self.__find_zeros(count, start, max_refine, rank, message_stamp, &result)
+ sig_off()
+ returnvalue = []
+ for i in range(result.size()):
+@@ -390,7 +392,7 @@ cdef class Lfunction:
+ cdef void __find_zeros_v(self,double T1, double T2, double stepsize, doublevec *result):
+ raise NotImplementedError
+
+- cdef void __find_zeros_via_N_v(self, long count,int do_negative,double max_refine, int rank, int test_explicit_formula, doublevec *result):
++ cdef int __find_zeros(self, long count, long start, double max_refine, int rank, const char* message_stamp, doublevec *result):
+ raise NotImplementedError
+
+ ##############################################################################
+@@ -486,8 +488,8 @@ cdef class Lfunction_I(Lfunction):
+ cdef double __typedN(self, double T):
+ return (<c_Lfunction_I *>self.thisptr).N(T)
+
+- cdef void __find_zeros_via_N_v(self, long count,int do_negative,double max_refine, int rank, int test_explicit_formula, doublevec *result):
+- (<c_Lfunction_I *>self.thisptr).find_zeros_via_N_v(count, do_negative, max_refine, rank, test_explicit_formula, result[0])
++ cdef int __find_zeros(self, long count, long start, double max_refine, int rank, const char* message_stamp, doublevec *result):
++ (<c_Lfunction_I *>self.thisptr).find_zeros(count, start, max_refine, rank, message_stamp, result)
+
+ # debug tools
+ def _print_data_to_standard_output(self):
+@@ -500,7 +502,7 @@ cdef class Lfunction_I(Lfunction):
+ sage: from sage.libs.lcalc.lcalc_Lfunction import *
+ sage: chi = DirichletGroup(5)[2] #This is a quadratic character
+ sage: L=Lfunction_from_character(chi, type="int")
+- sage: L._print_data_to_standard_output() # tol 1e-15
++ sage: L._print_data_to_standard_output() # tol 1e-8
+ -----------------------------------------------
+ <BLANKLINE>
+ Name of L_function:
+@@ -624,8 +626,8 @@ cdef class Lfunction_D(Lfunction):
+ cdef double __typedN(self, double T):
+ return (<c_Lfunction_D *>self.thisptr).N(T)
+
+- cdef void __find_zeros_via_N_v(self, long count,int do_negative,double max_refine, int rank, int test_explicit_formula, doublevec *result):
+- (<c_Lfunction_D *>self.thisptr).find_zeros_via_N_v(count, do_negative, max_refine, rank, test_explicit_formula, result[0])
++ cdef int __find_zeros(self, long count, long start,double max_refine, int rank, const char* message_stamp, doublevec *result):
++ (<c_Lfunction_D *>self.thisptr).find_zeros(count, start, max_refine, rank, message_stamp, result)
+
+ # debug tools
+ def _print_data_to_standard_output(self):
+@@ -638,7 +640,7 @@ cdef class Lfunction_D(Lfunction):
+ sage: from sage.libs.lcalc.lcalc_Lfunction import *
+ sage: chi = DirichletGroup(5)[2] #This is a quadratic character
+ sage: L=Lfunction_from_character(chi, type="double")
+- sage: L._print_data_to_standard_output() # tol 1e-15
++ sage: L._print_data_to_standard_output() # tol 1e-8
+ -----------------------------------------------
+ <BLANKLINE>
+ Name of L_function:
+@@ -769,8 +771,8 @@ cdef class Lfunction_C:
+ cdef double __typedN(self, double T):
+ return (<c_Lfunction_C *>self.thisptr).N(T)
+
+- cdef void __find_zeros_via_N_v(self, long count,int do_negative,double max_refine, int rank, int test_explicit_formula, doublevec *result):
+- (<c_Lfunction_C *>self.thisptr).find_zeros_via_N_v(count, do_negative, max_refine, rank, test_explicit_formula, result[0])
++ cdef int __find_zeros(self, long count, long start, double max_refine, int rank, const char* message_stamp, doublevec *result):
++ (<c_Lfunction_C *>self.thisptr).find_zeros(count, start, max_refine, rank, message_stamp, result)
+
+ # debug tools
+ def _print_data_to_standard_output(self):
+@@ -783,7 +785,7 @@ cdef class Lfunction_C:
+ sage: from sage.libs.lcalc.lcalc_Lfunction import *
+ sage: chi = DirichletGroup(5)[1]
+ sage: L=Lfunction_from_character(chi, type="complex")
+- sage: L._print_data_to_standard_output() # tol 1e-15
++ sage: L._print_data_to_standard_output() # tol 1e-8
+ -----------------------------------------------
+ <BLANKLINE>
+ Name of L_function:
+@@ -854,8 +856,8 @@ cdef class Lfunction_Zeta(Lfunction):
+ cdef double __typedN(self, double T):
+ return (<c_Lfunction_Zeta *>self.thisptr).N(T)
+
+- cdef void __find_zeros_via_N_v(self, long count,int do_negative,double max_refine, int rank, int test_explicit_formula, doublevec *result):
+- (<c_Lfunction_Zeta *>self.thisptr).find_zeros_via_N_v(count, do_negative, max_refine, rank, test_explicit_formula, result[0])
++ cdef int __find_zeros(self, long count, long start, double max_refine, int rank, const char* message_stamp, doublevec *result):
++ (<c_Lfunction_Zeta *>self.thisptr).find_zeros(count, start, max_refine, rank, message_stamp, result)
+
+ def __dealloc__(self):
+ """
+@@ -950,10 +952,11 @@ def Lfunction_from_elliptic_curve(E, number_of_coeffs=10000):
+ sage: L = Lfunction_from_elliptic_curve(EllipticCurve('37'))
+ sage: L
+ L-function with real Dirichlet coefficients
+- sage: L.value(0.5).abs() < 1e-15 # "noisy" zero on some platforms (see #9615)
++ sage: L.value(0.5).abs() < 1e-8 # "noisy" zero on some platforms (see #9615)
+ True
+- sage: L.value(0.5, derivative=1)
+- 0.305999...
++ sage: L.value(0.5, derivative=1) # abs tol 1e-6
++ 0.305999773835200 + 0.0*I
++
+ """
+ import sage.libs.lcalc.lcalc_Lfunction
+ Q = RRR(E.conductor()).sqrt() / RRR(2 * pi)
+diff --git a/src/sage/libs/lcalc/lcalc_sage.h b/src/sage/libs/lcalc/lcalc_sage.h
+index 4985289..891a40c 100644
+--- a/src/sage/libs/lcalc/lcalc_sage.h
++++ b/src/sage/libs/lcalc/lcalc_sage.h
+@@ -1,4 +1,4 @@
+-#include "Lfunction/L.h"
++#include "lcalc/L.h"
+ int *new_ints(int l)
+ {
+ return new int[l];
+@@ -62,4 +62,3 @@ void testL(L_function<Complex> *L)
+ cout << "Value at 1" << L->value(1.0) <<endl;
+ cout << "Value at .5+I" << L->value(.5+I) <<endl;
+ }
+-
+diff --git a/src/sage/modular/dirichlet.py b/src/sage/modular/dirichlet.py
+index d101f6a..23a9b1b 100644
+--- a/src/sage/modular/dirichlet.py
++++ b/src/sage/modular/dirichlet.py
+@@ -751,8 +751,8 @@ class DirichletCharacter(MultiplicativeGroupElement):
+ sage: a = a.primitive_character()
+ sage: L = a.lfunction(algorithm='lcalc'); L
+ L-function with complex Dirichlet coefficients
+- sage: L.value(4) # abs tol 1e-14
+- 0.988944551741105 - 5.16608739123418e-18*I
++ sage: L.value(4) # abs tol 1e-8
++ 0.988944551741105 + 0.0*I
+ """
+ if algorithm is None:
+ algorithm = 'pari'
+diff --git a/src/sage/schemes/elliptic_curves/ell_rational_field.py b/src/sage/schemes/elliptic_curves/ell_rational_field.py
+index bda999e..1736ce4 100644
+--- a/src/sage/schemes/elliptic_curves/ell_rational_field.py
++++ b/src/sage/schemes/elliptic_curves/ell_rational_field.py
+@@ -1529,7 +1529,7 @@ class EllipticCurve_rational_field(EllipticCurve_number_field):
+ sage: EllipticCurve([1234567,89101112]).analytic_rank(algorithm='rubinstein')
+ Traceback (most recent call last):
+ ...
+- RuntimeError: unable to compute analytic rank using rubinstein algorithm (unable to convert ' 6.19283e+19 and is too large' to an integer)
++ RuntimeError: unable to compute analytic rank using rubinstein algorithm (unable to convert ' 6.19283... and is too large' to an integer)
+ sage: EllipticCurve([1234567,89101112]).analytic_rank(algorithm='sympow')
+ Traceback (most recent call last):
+ ...
+diff --git a/src/sage/schemes/elliptic_curves/lseries_ell.py b/src/sage/schemes/elliptic_curves/lseries_ell.py
+index 1fcd02f..8536db5 100644
+--- a/src/sage/schemes/elliptic_curves/lseries_ell.py
++++ b/src/sage/schemes/elliptic_curves/lseries_ell.py
+@@ -400,8 +400,22 @@ class Lseries_ell(SageObject):
+
+ sage: E = EllipticCurve('37a')
+ sage: vals = E.lseries().twist_values(1, -12, -4)
+- sage: vals # abs tol 1e-15
+- [(-11, 1.47824342), (-8, 8.9590946e-18), (-7, 1.85307619), (-4, 2.45138938)]
++ sage: vals[0][0]
++ -11
++ sage: vals[0][1] # abs tol 1e-8
++ 1.47824342 + 0.0*I
++ sage: vals[1][0]
++ -8
++ sage: vals[1][1] # abs tol 1e-8
++ 0.0 + 0.0*I
++ sage: vals[2][0]
++ -7
++ sage: vals[2][1] # abs tol 1e-8
++ 1.85307619 + 0.0*I
++ sage: vals[3][0]
++ -4
++ sage: vals[3][1] # abs tol 1e-8
++ 2.45138938 + 0.0*I
+ sage: F = E.quadratic_twist(-8)
+ sage: F.rank()
+ 1
+