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# List of coset representatives for \(\Gamma_H(N)\) in \({\rm SL}_2(\ZZ)\)

class `sage.modular.modsym.ghlist.``GHlist`(group)

  A class representing a list of coset representatives for \(\Gamma_H(N)\) in \({\rm SL}_2(\ZZ)\).

  TESTS:

      sage: L = sage.modular.modsym.ghlist.GHlist(GammaH(18,[13]))
      sage: loads(dumps(L)) == L
      True

  `list`()

    Return a list of vectors representing the cosets. Do not change the returned list!

    EXAMPLE:

        sage: L = sage.modular.modsym.ghlist.GHlist(GammaH(4,[])); L.list()
        [(0, 1), (0, 3), (1, 0), (1, 1), (1, 2), (1, 3), (2, 1), (2, 3), (3, 0), (3, 1), (3, 2), (3, 3)]

  `normalize`(u, v)

    Given a pair \((u,v)\) of integers, return the unique pair \((u', v')\) such that the pair \((u', v')\) appears in `self.list()` and \((u, v)\) is equivalent to \((u', v')\).

    This will only make sense if \({\rm gcd}(u, v, N) = 1\); otherwise the output will not be an element of self.

    EXAMPLES:

        sage: sage.modular.modsym.ghlist.GHlist(GammaH(24, [17, 19])).normalize(17, 6)
        (1, 6)
        sage: sage.modular.modsym.ghlist.GHlist(GammaH(24, [7, 13])).normalize(17, 6)
        (5, 6)
        sage: sage.modular.modsym.ghlist.GHlist(GammaH(24, [5, 23])).normalize(17, 6)
        (7, 18)

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