Properties

Label 15.26
Level $15$
Weight $0$
Character 15.1
Symmetry even
\(R\) 6.180431
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: \(6.18043116287990243185791813716 \pm 4 \cdot 10^{-11}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +0.08204923 \pm 1 \cdot 10^{-8} \) \(a_{3}= -0.57735027 \pm 1.0 \cdot 10^{-8} \)
\(a_{4}= -0.99326792 \pm 1 \cdot 10^{-8} \) \(a_{5}= -0.44721360 \pm 1.0 \cdot 10^{-8} \) \(a_{6}= -0.04737114 \pm 1.0 \cdot 10^{-8} \)
\(a_{7}= +0.12447779 \pm 1 \cdot 10^{-8} \) \(a_{8}= -0.16354609 \pm 1 \cdot 10^{-8} \) \(a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8} \)
\(a_{10}= -0.03669353 \pm 1.0 \cdot 10^{-8} \) \(a_{11}= +0.83069280 \pm 1 \cdot 10^{-8} \) \(a_{12}= +0.57346350 \pm 1.0 \cdot 10^{-8} \)
\(a_{13}= +1.25303715 \pm 1 \cdot 10^{-8} \) \(a_{14}= +0.01021331 \pm 1 \cdot 10^{-8} \) \(a_{15}= +0.25819889 \pm 1.0 \cdot 10^{-8} \)
\(a_{16}= +0.97984909 \pm 1 \cdot 10^{-8} \) \(a_{17}= -1.07113921 \pm 1 \cdot 10^{-8} \) \(a_{18}= +0.02734974 \pm 1.0 \cdot 10^{-8} \)
\(a_{19}= -0.22422753 \pm 1 \cdot 10^{-8} \) \(a_{20}= +0.44420292 \pm 1.0 \cdot 10^{-8} \) \(a_{21}= -0.07186728 \pm 1.0 \cdot 10^{-8} \)
\(a_{22}= +0.06815770 \pm 1 \cdot 10^{-8} \) \(a_{23}= +0.47445189 \pm 1 \cdot 10^{-8} \) \(a_{24}= +0.09442338 \pm 1.0 \cdot 10^{-8} \)
\(a_{25}= +0.2 \) \(a_{26}= +0.10281073 \pm 1 \cdot 10^{-8} \) \(a_{27}= -0.19245009 \pm 9.4 \cdot 10^{-8} \)
\(a_{28}= -0.12363979 \pm 1 \cdot 10^{-8} \) \(a_{29}= +1.49583123 \pm 1 \cdot 10^{-8} \) \(a_{30}= +0.02118502 \pm 1.0 \cdot 10^{-8} \)
\(a_{31}= -1.06256248 \pm 1 \cdot 10^{-8} \) \(a_{32}= +0.24394195 \pm 1 \cdot 10^{-8} \) \(a_{33}= -0.47960071 \pm 1.0 \cdot 10^{-8} \)
\(a_{34}= -0.08788614 \pm 1 \cdot 10^{-8} \) \(a_{35}= -0.05566816 \pm 1.0 \cdot 10^{-8} \) \(a_{36}= -0.33108931 \pm 1.0 \cdot 10^{-8} \)
\(a_{37}= -0.72395893 \pm 1 \cdot 10^{-8} \) \(a_{38}= -0.01839769 \pm 1 \cdot 10^{-8} \) \(a_{39}= -0.72344134 \pm 1.0 \cdot 10^{-8} \)
\(a_{40}= +0.07314003 \pm 1.0 \cdot 10^{-8} \) \(a_{41}= +1.61035766 \pm 1 \cdot 10^{-8} \) \(a_{42}= -0.00589665 \pm 1.1 \cdot 10^{-8} \)
\(a_{43}= +1.77549092 \pm 1 \cdot 10^{-8} \) \(a_{44}= -0.82510052 \pm 1 \cdot 10^{-8} \) \(a_{45}= -0.14907120 \pm 1.4 \cdot 10^{-7} \)
\(a_{46}= +0.03892841 \pm 1 \cdot 10^{-8} \) \(a_{47}= +0.95237256 \pm 1 \cdot 10^{-8} \) \(a_{48}= -0.56571614 \pm 1.0 \cdot 10^{-8} \)
\(a_{49}= -0.98450528 \pm 1 \cdot 10^{-8} \) \(a_{50}= +0.01640985 \pm 1.0 \cdot 10^{-8} \) \(a_{51}= +0.61842251 \pm 1.0 \cdot 10^{-8} \)
\(a_{52}= -1.24460161 \pm 1 \cdot 10^{-8} \) \(a_{53}= +1.14398690 \pm 1 \cdot 10^{-8} \) \(a_{54}= -0.01579038 \pm 1.0 \cdot 10^{-8} \)
\(a_{55}= -0.37149712 \pm 1.0 \cdot 10^{-8} \) \(a_{56}= -0.02035786 \pm 1 \cdot 10^{-8} \) \(a_{57}= +0.12945782 \pm 1.0 \cdot 10^{-8} \)
\(a_{58}= +0.12273179 \pm 1 \cdot 10^{-8} \) \(a_{59}= -0.35192129 \pm 1 \cdot 10^{-8} \) \(a_{60}= -0.25646068 \pm 1.0 \cdot 10^{-8} \)

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