Properties

Label 15.6
Level $15$
Weight $0$
Character 15.1
Symmetry odd
\(R\) 3.104500
Fricke sign $-1$

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Maass form invariants

Level: \( 15 = 3 \cdot 5 \)
Weight: \( 0 \)
Character: 15.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \(3.10450058521073190818804678447 \pm 7 \cdot 10^{-12}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +1.40057911 \pm 1 \cdot 10^{-8} \) \(a_{3}= +0.57735027 \pm 1.0 \cdot 10^{-8} \)
\(a_{4}= +0.96162184 \pm 1 \cdot 10^{-8} \) \(a_{5}= -0.44721360 \pm 1.0 \cdot 10^{-8} \) \(a_{6}= +0.80862472 \pm 1.2 \cdot 10^{-8} \)
\(a_{7}= -0.79844062 \pm 1 \cdot 10^{-8} \) \(a_{8}= -0.05375165 \pm 1 \cdot 10^{-8} \) \(a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8} \)
\(a_{10}= -0.62635802 \pm 1.2 \cdot 10^{-8} \) \(a_{11}= +0.68234362 \pm 1 \cdot 10^{-8} \) \(a_{12}= +0.55519263 \pm 1.2 \cdot 10^{-8} \)
\(a_{13}= +1.95752907 \pm 1 \cdot 10^{-8} \) \(a_{14}= -1.11827925 \pm 1 \cdot 10^{-8} \) \(a_{15}= -0.25819889 \pm 1.0 \cdot 10^{-8} \)
\(a_{16}= -1.03690528 \pm 1 \cdot 10^{-8} \) \(a_{17}= -1.18150975 \pm 1 \cdot 10^{-8} \) \(a_{18}= +0.46685970 \pm 1.2 \cdot 10^{-8} \)
\(a_{19}= +0.23992205 \pm 1 \cdot 10^{-8} \) \(a_{20}= -0.43005036 \pm 1.2 \cdot 10^{-8} \) \(a_{21}= -0.46097990 \pm 1.2 \cdot 10^{-8} \)
\(a_{22}= +0.95567622 \pm 1 \cdot 10^{-8} \) \(a_{23}= +0.00554965 \pm 1 \cdot 10^{-8} \) \(a_{24}= -0.03103353 \pm 1.2 \cdot 10^{-8} \)
\(a_{25}= +0.2 \) \(a_{26}= +2.74167431 \pm 1 \cdot 10^{-8} \) \(a_{27}= +0.19245009 \pm 9.4 \cdot 10^{-8} \)
\(a_{28}= -0.76779793 \pm 1 \cdot 10^{-8} \) \(a_{29}= -0.63881725 \pm 1 \cdot 10^{-8} \) \(a_{30}= -0.36162797 \pm 1.2 \cdot 10^{-8} \)
\(a_{31}= -0.15346815 \pm 1 \cdot 10^{-8} \) \(a_{32}= -1.39851622 \pm 1 \cdot 10^{-8} \) \(a_{33}= +0.39395127 \pm 1.2 \cdot 10^{-8} \)
\(a_{34}= -1.65479788 \pm 1 \cdot 10^{-8} \) \(a_{35}= +0.35707350 \pm 1.2 \cdot 10^{-8} \) \(a_{36}= +0.32054061 \pm 1.2 \cdot 10^{-8} \)
\(a_{37}= +0.66994276 \pm 1 \cdot 10^{-8} \) \(a_{38}= +0.33602981 \pm 1 \cdot 10^{-8} \) \(a_{39}= +1.13017993 \pm 1.2 \cdot 10^{-8} \)
\(a_{40}= +0.02403847 \pm 1.2 \cdot 10^{-8} \) \(a_{41}= -1.23681028 \pm 1 \cdot 10^{-8} \) \(a_{42}= -0.64563882 \pm 1.5 \cdot 10^{-8} \)
\(a_{43}= +1.03784093 \pm 1 \cdot 10^{-8} \) \(a_{44}= +0.65615653 \pm 1 \cdot 10^{-8} \) \(a_{45}= -0.14907120 \pm 1.4 \cdot 10^{-7} \)
\(a_{46}= +0.00777272 \pm 1 \cdot 10^{-8} \) \(a_{47}= -0.54921153 \pm 1 \cdot 10^{-8} \) \(a_{48}= -0.59865754 \pm 1.2 \cdot 10^{-8} \)
\(a_{49}= -0.36249258 \pm 1 \cdot 10^{-8} \) \(a_{50}= +0.28011582 \pm 1.2 \cdot 10^{-8} \) \(a_{51}= -0.68214497 \pm 1.2 \cdot 10^{-8} \)
\(a_{52}= +1.88240269 \pm 1 \cdot 10^{-8} \) \(a_{53}= +1.12073576 \pm 1 \cdot 10^{-8} \) \(a_{54}= +0.26954157 \pm 1.2 \cdot 10^{-8} \)
\(a_{55}= -0.30515335 \pm 1.2 \cdot 10^{-8} \) \(a_{56}= +0.04291750 \pm 1 \cdot 10^{-8} \) \(a_{57}= +0.13851906 \pm 1.2 \cdot 10^{-8} \)
\(a_{58}= -0.89471409 \pm 1 \cdot 10^{-8} \) \(a_{59}= -0.09045217 \pm 1 \cdot 10^{-8} \) \(a_{60}= -0.24828969 \pm 1.2 \cdot 10^{-8} \)

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