Properties

Label 5.48
Level $5$
Weight $0$
Character 5.1
Symmetry odd
\(R\) 13.57514
Fricke sign $+1$

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Maass form invariants

Level: \( 5 \)
Weight: \( 0 \)
Character: 5.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \(13.5751469722125384701318658932 \pm 6 \cdot 10^{-9}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -1.77264780 \pm 7.1 \cdot 10^{-6} \) \(a_{3}= +1.65091832 \pm 7.7 \cdot 10^{-6} \)
\(a_{4}= +2.14228021 \pm 6.2 \cdot 10^{-6} \) \(a_{5}= -0.44721360 \pm 1.0 \cdot 10^{-8} \) \(a_{6}= -2.92649673 \pm 7.3 \cdot 10^{-6} \)
\(a_{7}= -0.37903577 \pm 2.9 \cdot 10^{-6} \) \(a_{8}= -2.02486051 \pm 6.6 \cdot 10^{-6} \) \(a_{9}= +1.72553131 \pm 3.7 \cdot 10^{-6} \)
\(a_{10}= +0.79275220 \pm 7.1 \cdot 10^{-6} \) \(a_{11}= -1.17938046 \pm 3.9 \cdot 10^{-6} \) \(a_{12}= +3.53672966 \pm 6.4 \cdot 10^{-6} \)
\(a_{13}= -0.12677608 \pm 5.0 \cdot 10^{-6} \) \(a_{14}= +0.67189693 \pm 3.0 \cdot 10^{-6} \) \(a_{15}= -0.73831312 \pm 7.7 \cdot 10^{-6} \)
\(a_{16}= +1.44708430 \pm 3.1 \cdot 10^{-6} \) \(a_{17}= +0.22158530 \pm 7.9 \cdot 10^{-6} \) \(a_{18}= -3.05875927 \pm 3.3 \cdot 10^{-6} \)
\(a_{19}= +0.43589052 \pm 7.3 \cdot 10^{-6} \) \(a_{20}= -0.95805684 \pm 6.2 \cdot 10^{-6} \) \(a_{21}= -0.62575710 \pm 3.2 \cdot 10^{-6} \)
\(a_{22}= +2.09062617 \pm 4.2 \cdot 10^{-6} \) \(a_{23}= -1.14188714 \pm 3.0 \cdot 10^{-6} \) \(a_{24}= -3.34287931 \pm 6.9 \cdot 10^{-6} \)
\(a_{25}= +0.2 \) \(a_{26}= +0.22472933 \pm 6.0 \cdot 10^{-6} \) \(a_{27}= +1.19779293 \pm 5.9 \cdot 10^{-6} \)
\(a_{28}= -0.81200084 \pm 2.4 \cdot 10^{-6} \) \(a_{29}= -0.34369638 \pm 3.6 \cdot 10^{-6} \) \(a_{30}= +1.30876912 \pm 1.4 \cdot 10^{-5} \)
\(a_{31}= -0.32124002 \pm 7.6 \cdot 10^{-6} \) \(a_{32}= -0.54031030 \pm 7.7 \cdot 10^{-6} \) \(a_{33}= -1.94706080 \pm 2.8 \cdot 10^{-6} \)
\(a_{34}= -0.39279269 \pm 7.5 \cdot 10^{-6} \) \(a_{35}= +0.16950995 \pm 2.9 \cdot 10^{-6} \) \(a_{36}= +3.69657158 \pm 1.7 \cdot 10^{-6} \)
\(a_{37}= -1.30109525 \pm 9.4 \cdot 10^{-6} \) \(a_{38}= -0.77268036 \pm 5.1 \cdot 10^{-6} \) \(a_{39}= -0.20929695 \pm 4.0 \cdot 10^{-6} \)
\(a_{40}= +0.90554515 \pm 6.6 \cdot 10^{-6} \) \(a_{41}= -1.58967132 \pm 8.1 \cdot 10^{-6} \) \(a_{42}= +1.10924695 \pm 3.0 \cdot 10^{-6} \)
\(a_{43}= +1.26867000 \pm 8.0 \cdot 10^{-6} \) \(a_{44}= -2.52656342 \pm 3.0 \cdot 10^{-6} \) \(a_{45}= -0.77168106 \pm 3.8 \cdot 10^{-6} \)
\(a_{46}= +2.02416373 \pm 3.7 \cdot 10^{-6} \) \(a_{47}= -1.49696719 \pm 4.7 \cdot 10^{-6} \) \(a_{48}= +2.38901799 \pm 3.2 \cdot 10^{-6} \)
\(a_{49}= -0.85633188 \pm 6.4 \cdot 10^{-6} \) \(a_{50}= -0.35452956 \pm 7.1 \cdot 10^{-6} \) \(a_{51}= +0.36581923 \pm 7.7 \cdot 10^{-6} \)
\(a_{52}= -0.27158988 \pm 4.8 \cdot 10^{-6} \) \(a_{53}= +0.91226476 \pm 7.5 \cdot 10^{-6} \) \(a_{54}= -2.12326500 \pm 6.1 \cdot 10^{-6} \)
\(a_{55}= +0.52743497 \pm 3.9 \cdot 10^{-6} \) \(a_{56}= +0.76749457 \pm 2.6 \cdot 10^{-6} \) \(a_{57}= +0.71961964 \pm 8.5 \cdot 10^{-6} \)
\(a_{58}= +0.60925263 \pm 2.8 \cdot 10^{-6} \) \(a_{59}= -0.66326051 \pm 6.0 \cdot 10^{-6} \) \(a_{60}= -1.58167359 \pm 1.3 \cdot 10^{-5} \)

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