Properties

Label 5.47
Level $5$
Weight $0$
Character 5.1
Symmetry even
\(R\) 13.46898
Fricke sign $+1$

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Maass form invariants

Level: \( 5 \)
Weight: \( 0 \)
Character: 5.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \(13.4689817279077632395708438097 \pm 5 \cdot 10^{-9}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +0.28850745 \pm 1.0 \cdot 10^{-8} \) \(a_{3}= +1.81176018 \pm 1 \cdot 10^{-8} \)
\(a_{4}= -0.91676345 \pm 1.0 \cdot 10^{-8} \) \(a_{5}= -0.44721360 \pm 1.0 \cdot 10^{-8} \) \(a_{6}= +0.52270631 \pm 1 \cdot 10^{-8} \)
\(a_{7}= +1.05569799 \pm 1.1 \cdot 10^{-8} \) \(a_{8}= -0.55300054 \pm 1.3 \cdot 10^{-8} \) \(a_{9}= +2.28247495 \pm 1 \cdot 10^{-8} \)
\(a_{10}= -0.12902446 \pm 2.1 \cdot 10^{-8} \) \(a_{11}= +0.66805106 \pm 1.3 \cdot 10^{-8} \) \(a_{12}= -1.66095551 \pm 1 \cdot 10^{-8} \)
\(a_{13}= +0.43699604 \pm 1.0 \cdot 10^{-8} \) \(a_{14}= +0.30457674 \pm 1.0 \cdot 10^{-8} \) \(a_{15}= -0.81024378 \pm 1.9 \cdot 10^{-8} \)
\(a_{16}= +0.75721867 \pm 1.0 \cdot 10^{-8} \) \(a_{17}= +0.20056032 \pm 1 \cdot 10^{-8} \) \(a_{18}= +0.65851103 \pm 1 \cdot 10^{-8} \)
\(a_{19}= +0.41978546 \pm 1 \cdot 10^{-8} \) \(a_{20}= +0.40998908 \pm 2.1 \cdot 10^{-8} \) \(a_{21}= +1.91267158 \pm 1 \cdot 10^{-8} \)
\(a_{22}= +0.19273771 \pm 1.0 \cdot 10^{-8} \) \(a_{23}= +0.43917938 \pm 1 \cdot 10^{-8} \) \(a_{24}= -1.00190436 \pm 1 \cdot 10^{-8} \)
\(a_{25}= +0.2 \) \(a_{26}= +0.12607661 \pm 1 \cdot 10^{-8} \) \(a_{27}= +2.32353704 \pm 1.2 \cdot 10^{-8} \)
\(a_{28}= -0.96782533 \pm 1 \cdot 10^{-8} \) \(a_{29}= +0.89425740 \pm 1.3 \cdot 10^{-8} \) \(a_{30}= -0.23376137 \pm 3.0 \cdot 10^{-8} \)
\(a_{31}= -1.78704214 \pm 1 \cdot 10^{-8} \) \(a_{32}= +0.77146377 \pm 1 \cdot 10^{-8} \) \(a_{33}= +1.21034830 \pm 1.0 \cdot 10^{-8} \)
\(a_{34}= +0.05786315 \pm 1 \cdot 10^{-8} \) \(a_{35}= -0.47212249 \pm 2.2 \cdot 10^{-8} \) \(a_{36}= -2.09248961 \pm 1 \cdot 10^{-8} \)
\(a_{37}= +1.69406117 \pm 1.3 \cdot 10^{-8} \) \(a_{38}= +0.12111123 \pm 1 \cdot 10^{-8} \) \(a_{39}= +0.79173202 \pm 1 \cdot 10^{-8} \)
\(a_{40}= +0.24730936 \pm 2.4 \cdot 10^{-8} \) \(a_{41}= -0.25467131 \pm 1 \cdot 10^{-8} \) \(a_{42}= +0.55182001 \pm 1 \cdot 10^{-8} \)
\(a_{43}= -1.13084618 \pm 1 \cdot 10^{-8} \) \(a_{44}= -0.61244479 \pm 1 \cdot 10^{-8} \) \(a_{45}= -1.02075383 \pm 1.6 \cdot 10^{-8} \)
\(a_{46}= +0.12670652 \pm 1 \cdot 10^{-8} \) \(a_{47}= +0.60659433 \pm 1.2 \cdot 10^{-8} \) \(a_{48}= +1.37189864 \pm 1 \cdot 10^{-8} \)
\(a_{49}= +0.11449825 \pm 1 \cdot 10^{-8} \) \(a_{50}= +0.05770149 \pm 2.1 \cdot 10^{-8} \) \(a_{51}= +0.36336721 \pm 1 \cdot 10^{-8} \)
\(a_{52}= -0.40062200 \pm 1.0 \cdot 10^{-8} \) \(a_{53}= -1.05830836 \pm 1 \cdot 10^{-8} \) \(a_{54}= +0.67035775 \pm 1 \cdot 10^{-8} \)
\(a_{55}= -0.29876151 \pm 2.4 \cdot 10^{-8} \) \(a_{56}= -0.58380156 \pm 1.3 \cdot 10^{-8} \) \(a_{57}= +0.76055058 \pm 1 \cdot 10^{-8} \)
\(a_{58}= +0.25799992 \pm 1.3 \cdot 10^{-8} \) \(a_{59}= -1.36745789 \pm 1 \cdot 10^{-8} \) \(a_{60}= +0.74280189 \pm 3.0 \cdot 10^{-8} \)

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