\label{rw:sec:notation}
The table lists notation used in more than one section, with the
place where it is introduced.

\begingroup
\small
\renewcommand{\arraystretch}{1.13}
\begin{longtable}{@{}>{\raggedright\arraybackslash}p{.24\textwidth}
                    >{\raggedright\arraybackslash}p{.72\textwidth}@{}}
\toprule
Notation & Meaning and location \\
\midrule
\endfirsthead
\toprule
Notation & Meaning and location \\
\midrule
\endhead
\bottomrule
\endfoot
\(X,F,\Gamma_F,W_F\) & The original curve, its function field, its
absolute Galois group and its Weil group
(Sections~\ref{fl:sec:introduction} and~\ref{fl:sec:parameters-parameters}).\\
\(p,q,\ell,k\) & The geometric characteristic, size of the constant
field, coefficient prime, and \(k=\overline{\mathbb Q}_\ell\).\\
\(E,\mathcal O_E\) & A finite extension of \(\mathbb Q_\ell\) and
its ring of integers (Section~\ref{fl:sec:compact-foundations}).\\
\(\deg_F,d_v\) & Arithmetic Galois degree and the degree of a closed
point \(v\); geometric Frobenius at \(v\) has degree \(-d_v\).\\
\(\operatorname{Fr}_q,\Frob_q\) & The \(q\)-power map of a scheme
and geometric Frobenius acting on sheaf cohomology, respectively.\\
\(G,\widehat G,M,\widehat M\) & The split group, its dual, a Levi
subgroup and the corresponding dual Levi.\\
\(K_N,\mathscr H_{G,u,\mathcal O_E}\) & The open compact subgroup
of level \(N\) and the integral spherical Hecke algebra at
\(u\notin N\)
(Section~\ref{fl:sec:compact-foundations}).\\
\(\sigma,\nu_\sigma\) & The prescribed parameter and its character
on excursion data, defined by \eqref{fl:eq:main-full-label}.\\
\(\vartheta_G,\sigma^\dagger\) & The Chevalley involution
preserving the pinning, and \(\vartheta_G\sigma\)
(Section~\ref{fl:sec:parameters-parameters}).\\
\(T_G,\Xi,\omega_\sigma\) & The connected centre with its reduced
structure, a central lattice, and the central character of
\(\sigma\) (Definition~\ref{fl:def:central-period-lattice}).\\
\(Q_G,\alpha_G,\beta_G\) & The quotient \(G/G_{\mathrm{der}}\) and
the homomorphisms \(\widehat G\to\widehat T_G\),
\(\widehat G\to\widehat{G_{\mathrm{der}}}\)
\eqref{fl:eq:two-central-maps}.\\
\(\mathsf a\) & The isogeny of dual groups dual to a central
isogeny \(H_0\to G\) (Section~\ref{fl:sec:arithmetic-central}).\\
\(\mathcal A_\Xi(G),\mathcal A^{\rm cont}(G)\) & The functions
invariant under \(\Xi\) with a finite integral spherical orbit, and
the span of the twists of such functions by characters of the
degree
(Definition~\ref{fl:def:parameter-independent-spaces}).\\
\(Y_N,C_{N,\mathcal O}\) & The double coset space of level \(N\)
and the functions with compact support on it
(Section~\ref{fl:sec:compact-foundations}).\\
\(e=(I,f,\boldsymbol\gamma),\ e^\star\) & An excursion datum and
its transpose (Definition~\ref{fl:def:weil-excursion-datum}).\\
\(S_e,S_e^{\mathrm{fun}}\) & The excursion operator on functions
with compact support, and its extension to all functions of finite
level (Definition~\ref{fl:def:function-excursion-action}).\\
\(\mathcal Q_{N,\Xi,u,\mathfrak a}\) & A finite Hecke quotient
(Definition~\ref{fl:def:finite-hecke-model}).\\
\(T_\psi\) & Multiplication by the class-field character of a
central parameter \(\psi\)
(Proposition~\ref{fl:prop:compact-central-twists}).\\
\(c^{\deg_F}\) & The twist by a unit point \(c\) of
\(Z(\widehat G)^\circ\)
(Definition~\ref{fl:def:constant-field-central-homomorphism}).\\
\(\mathsf{CT}^{\mathrm{nor}}_P\) & The normalized constant term
(Section~\ref{fl:sec:constant-term}).\\
\(\iota\) & A fixed isomorphism \(k\simeq\mathbb C\) which maps
\(q^{1/2}\) to the positive square root of \(q\)
(Section~\ref{fl:sec:parameters-parameters}).\\
\end{longtable}
\endgroup

\medskip
The following terms are introduced in this paper, or are used in a
sense fixed here.

\begingroup
\small
\renewcommand{\arraystretch}{1.13}
\begin{longtable}{@{}>{\raggedright\arraybackslash}p{.42\textwidth}
                    >{\raggedright\arraybackslash}p{.54\textwidth}@{}}
\toprule
Term & Where it is defined \\
\midrule
\endfirsthead
\toprule
Term & Where it is defined \\
\midrule
\endhead
parameter; semisimple; elliptic &
Definition~\ref{fl:def:intro-parameter}\\
excursion datum; excursion character \(\nu_\sigma\) &
Section~\ref{fl:sec:introduction};
Definition~\ref{fl:def:weil-excursion-datum}\\
automorphic form & Section~\ref{fl:sec:introduction}, after
Theorem~\ref{fl:thm:semisimple-elliptic}\\
central lattice; invariant under \(\Xi\) &
Definition~\ref{fl:def:central-period-lattice}\\
excursion summand & Definition~\ref{fl:def:full-excursion-summand}\\
automorphic realization; to realize a parameter &
Section~\ref{fl:sec:introduction}, after \eqref{fl:eq:main-full-label}\\
arithmetic monodromy group; strongly pure of weight zero &
Section~\ref{fl:sec:arithmetic-purity};
Definition~\ref{fl:def:strong-purity}\\
unit point; twist by the field of constants &
Definition~\ref{fl:def:constant-field-central-homomorphism}\\
central lattice; periodization &
Section~\ref{fl:sec:compact-foundations}\\
functions with compact support &
Section~\ref{fl:sec:compact-foundations}\\
finite Hecke quotient; cofinite ideal &
Definition~\ref{fl:def:finite-hecke-model}\\
finite integral spherical orbit &
Definition~\ref{fl:def:finite-integral-orbit}\\
unit-valued Satake parameters &
Definition~\ref{fl:def:unit-satake-support}\\
generalized excursion character; for Weil tuples &
Definition~\ref{fl:def:locally-generalized-weil-label}\\
operator with finite rows & Section~\ref{fl:sec:constant-term}\\
\bottomrule
\end{longtable}
\endgroup