Properties

Label 29.49
Level $29$
Weight $0$
Character 29.1
Symmetry even
\(R\) 5.007121
Fricke sign $-1$

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Maass form invariants

Level: \( 29 \)
Weight: \( 0 \)
Character: 29.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \(5.00712110787253002064988699277 \pm 8 \cdot 10^{-10}\)

Maass form coefficients

The coefficients here are shown to at most $8$ digits of precision. Full precision coefficients are available in the downloads.

\(a_{1}= +1 \) \(a_{2}= -1.07996937 \pm 6.3 \cdot 10^{-8} \) \(a_{3}= -1.12953165 \pm 5.6 \cdot 10^{-8} \)
\(a_{4}= +0.16633383 \pm 6.5 \cdot 10^{-8} \) \(a_{5}= +1.05165831 \pm 5.4 \cdot 10^{-8} \) \(a_{6}= +1.21985958 \pm 6.2 \cdot 10^{-8} \)
\(a_{7}= -0.55564583 \pm 5.1 \cdot 10^{-8} \) \(a_{8}= +0.90033392 \pm 7.6 \cdot 10^{-8} \) \(a_{9}= +0.27584175 \pm 5.4 \cdot 10^{-8} \)
\(a_{10}= -1.13575876 \pm 6.0 \cdot 10^{-8} \) \(a_{11}= +1.58503265 \pm 5.0 \cdot 10^{-8} \) \(a_{12}= -0.18787933 \pm 5.5 \cdot 10^{-8} \)
\(a_{13}= -0.43820979 \pm 5.4 \cdot 10^{-8} \) \(a_{14}= +0.60008048 \pm 4.6 \cdot 10^{-8} \) \(a_{15}= -1.18788135 \pm 5.0 \cdot 10^{-8} \)
\(a_{16}= -1.13866689 \pm 8.1 \cdot 10^{-8} \) \(a_{17}= +0.09162519 \pm 5.0 \cdot 10^{-8} \) \(a_{18}= -0.29790064 \pm 7.0 \cdot 10^{-8} \)
\(a_{19}= -0.77149952 \pm 4.5 \cdot 10^{-8} \) \(a_{20}= +0.17492636 \pm 6.0 \cdot 10^{-8} \) \(a_{21}= +0.62761955 \pm 5.4 \cdot 10^{-8} \)
\(a_{22}= -1.71178670 \pm 5.6 \cdot 10^{-8} \) \(a_{23}= +0.84891636 \pm 5.2 \cdot 10^{-8} \) \(a_{24}= -1.01695566 \pm 6.4 \cdot 10^{-8} \)
\(a_{25}= +0.10598521 \pm 5.4 \cdot 10^{-8} \) \(a_{26}= +0.47325315 \pm 6.5 \cdot 10^{-8} \) \(a_{27}= +0.81795966 \pm 5.6 \cdot 10^{-8} \)
\(a_{28}= -0.09242270 \pm 4.4 \cdot 10^{-8} \) \(a_{29}= +0.18569534 \pm 1.0 \cdot 10^{-8} \) \(a_{30}= +1.28287547 \pm 6.0 \cdot 10^{-8} \)
\(a_{31}= -1.36305289 \pm 5.1 \cdot 10^{-8} \) \(a_{32}= +0.32939144 \pm 8.6 \cdot 10^{-8} \) \(a_{33}= -1.79034454 \pm 4.8 \cdot 10^{-8} \)
\(a_{34}= -0.09895239 \pm 6.5 \cdot 10^{-8} \) \(a_{35}= -0.58434956 \pm 5.8 \cdot 10^{-8} \) \(a_{36}= +0.04588182 \pm 6.9 \cdot 10^{-8} \)
\(a_{37}= +0.94407005 \pm 5.3 \cdot 10^{-8} \) \(a_{38}= +0.83319585 \pm 4.7 \cdot 10^{-8} \) \(a_{39}= +0.49497183 \pm 5.3 \cdot 10^{-8} \)
\(a_{40}= +0.94684365 \pm 7.1 \cdot 10^{-8} \) \(a_{41}= -0.89912804 \pm 5.0 \cdot 10^{-8} \) \(a_{42}= -0.67780989 \pm 5.0 \cdot 10^{-8} \)
\(a_{43}= -1.15967784 \pm 5.1 \cdot 10^{-8} \) \(a_{44}= +0.26364455 \pm 5.6 \cdot 10^{-8} \) \(a_{45}= +0.29009127 \pm 4.7 \cdot 10^{-8} \)
\(a_{46}= -0.91680366 \pm 5.2 \cdot 10^{-8} \) \(a_{47}= +0.33710144 \pm 4.8 \cdot 10^{-8} \) \(a_{48}= +1.28616029 \pm 6.7 \cdot 10^{-8} \)
\(a_{49}= -0.69125771 \pm 4.4 \cdot 10^{-8} \) \(a_{50}= -0.11446078 \pm 5.7 \cdot 10^{-8} \) \(a_{51}= -0.10349355 \pm 5.3 \cdot 10^{-8} \)
\(a_{52}= -0.07288911 \pm 7.4 \cdot 10^{-8} \) \(a_{53}= -1.96894033 \pm 5.5 \cdot 10^{-8} \) \(a_{54}= -0.88337138 \pm 7.2 \cdot 10^{-8} \)
\(a_{55}= +1.66691276 \pm 5.0 \cdot 10^{-8} \) \(a_{56}= -0.50026679 \pm 5.5 \cdot 10^{-8} \) \(a_{57}= +0.87143313 \pm 4.5 \cdot 10^{-8} \)
\(a_{58}= -0.20054528 \pm 7.3 \cdot 10^{-8} \) \(a_{59}= +1.59382818 \pm 4.8 \cdot 10^{-8} \) \(a_{60}= -0.19758486 \pm 5.8 \cdot 10^{-8} \)

Displaying $a_n$ with $n$ up to: 60 180 1000