Properties

Label 15.40
Level $15$
Weight $0$
Character 15.1
Symmetry even
\(R\) 7.562171
Fricke sign $-1$

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Maass form invariants

Level: \( 15 = 3 \cdot 5 \)
Weight: \( 0 \)
Character: 15.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \(7.56217196142289907783685343164 \pm 10 \cdot 10^{-11}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -0.92302105 \pm 1 \cdot 10^{-8} \) \(a_{3}= +0.57735027 \pm 1.0 \cdot 10^{-8} \)
\(a_{4}= -0.14803215 \pm 1 \cdot 10^{-8} \) \(a_{5}= -0.44721360 \pm 1.0 \cdot 10^{-8} \) \(a_{6}= -0.53290645 \pm 1.1 \cdot 10^{-8} \)
\(a_{7}= +0.33505200 \pm 1 \cdot 10^{-8} \) \(a_{8}= +1.05965783 \pm 1 \cdot 10^{-8} \) \(a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8} \)
\(a_{10}= +0.41278756 \pm 1.1 \cdot 10^{-8} \) \(a_{11}= +0.09873737 \pm 1 \cdot 10^{-8} \) \(a_{12}= -0.08546640 \pm 1.1 \cdot 10^{-8} \)
\(a_{13}= +0.87026032 \pm 1 \cdot 10^{-8} \) \(a_{14}= -0.30926004 \pm 1 \cdot 10^{-8} \) \(a_{15}= -0.25819889 \pm 1.0 \cdot 10^{-8} \)
\(a_{16}= -0.83005434 \pm 1 \cdot 10^{-8} \) \(a_{17}= -0.37810037 \pm 1 \cdot 10^{-8} \) \(a_{18}= -0.30767368 \pm 1.1 \cdot 10^{-8} \)
\(a_{19}= -1.90554406 \pm 1 \cdot 10^{-8} \) \(a_{20}= +0.06620199 \pm 1.1 \cdot 10^{-8} \) \(a_{21}= +0.19344236 \pm 1.1 \cdot 10^{-8} \)
\(a_{22}= -0.09113667 \pm 1 \cdot 10^{-8} \) \(a_{23}= -0.26149453 \pm 1 \cdot 10^{-8} \) \(a_{24}= +0.61179374 \pm 1.1 \cdot 10^{-8} \)
\(a_{25}= +0.2 \) \(a_{26}= -0.80326859 \pm 1 \cdot 10^{-8} \) \(a_{27}= +0.19245009 \pm 9.4 \cdot 10^{-8} \)
\(a_{28}= -0.04959847 \pm 1 \cdot 10^{-8} \) \(a_{29}= -0.48929170 \pm 1 \cdot 10^{-8} \) \(a_{30}= +0.23832301 \pm 1.1 \cdot 10^{-8} \)
\(a_{31}= -1.53573291 \pm 1 \cdot 10^{-8} \) \(a_{32}= -0.29350021 \pm 1 \cdot 10^{-8} \) \(a_{33}= +0.05700605 \pm 1.1 \cdot 10^{-8} \)
\(a_{34}= +0.34899460 \pm 1 \cdot 10^{-8} \) \(a_{35}= -0.14983981 \pm 1.1 \cdot 10^{-8} \) \(a_{36}= -0.04934405 \pm 1.1 \cdot 10^{-8} \)
\(a_{37}= -1.09065642 \pm 1 \cdot 10^{-8} \) \(a_{38}= +1.75885727 \pm 1 \cdot 10^{-8} \) \(a_{39}= +0.50244503 \pm 1.1 \cdot 10^{-8} \)
\(a_{40}= -0.47389339 \pm 1.1 \cdot 10^{-8} \) \(a_{41}= +1.28160014 \pm 1 \cdot 10^{-8} \) \(a_{42}= -0.17855137 \pm 1.2 \cdot 10^{-8} \)
\(a_{43}= +0.13175545 \pm 1 \cdot 10^{-8} \) \(a_{44}= -0.01461630 \pm 1 \cdot 10^{-8} \) \(a_{45}= -0.14907120 \pm 1.4 \cdot 10^{-7} \)
\(a_{46}= +0.24136495 \pm 1 \cdot 10^{-8} \) \(a_{47}= -1.10040937 \pm 1 \cdot 10^{-8} \) \(a_{48}= -0.47923210 \pm 1.1 \cdot 10^{-8} \)
\(a_{49}= -0.88774016 \pm 1 \cdot 10^{-8} \) \(a_{50}= -0.18460421 \pm 1.1 \cdot 10^{-8} \) \(a_{51}= -0.21829635 \pm 1.1 \cdot 10^{-8} \)
\(a_{52}= -0.12882650 \pm 1 \cdot 10^{-8} \) \(a_{53}= +1.30641856 \pm 1 \cdot 10^{-8} \) \(a_{54}= -0.17763548 \pm 1.1 \cdot 10^{-8} \)
\(a_{55}= -0.04415669 \pm 1.1 \cdot 10^{-8} \) \(a_{56}= +0.35504047 \pm 1 \cdot 10^{-8} \) \(a_{57}= -1.10016638 \pm 1.1 \cdot 10^{-8} \)
\(a_{58}= +0.45162654 \pm 1 \cdot 10^{-8} \) \(a_{59}= +1.28967818 \pm 1 \cdot 10^{-8} \) \(a_{60}= +0.03822174 \pm 1.1 \cdot 10^{-8} \)

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