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/*
Copyright (C) 2016 Pascal Molin
This file is part of FLINT.
FLINT is free software: you can redistribute it and/or modify it under
the terms of the GNU Lesser General Public License (LGPL) as published
by the Free Software Foundation; either version 3 of the License, or
(at your option) any later version. See <https://www.gnu.org/licenses/>.
*/
#include "dirichlet.h"
ulong
dirichlet_conductor_ui(const dirichlet_group_t G, ulong a)
{
slong k;
ulong ap, cond;
cond = 1;
for (k = (G->neven == 2); k < G->num; k++)
{
ulong p;
nmod_t pe;
p = G->P[k].p;
pe = G->P[k].pe;
ap = a % pe.n;
if (ap == 1)
continue;
if (p == 2)
{
cond = 4;
if (a % 4 == 3)
ap = pe.n - ap;
}
else
{
cond *= p;
ap = nmod_pow_ui(ap, p - 1, pe);
}
while (ap != 1)
{
cond *= p;
ap = nmod_pow_ui(ap, p, pe);
}
}
return cond;
}