Properties

Label 31.28
Level $31$
Weight $0$
Character 31.1
Symmetry odd
\(R\) 3.705939
Fricke sign $-1$

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Maass form invariants

Level: \( 31 \)
Weight: \( 0 \)
Character: 31.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \(3.70593927593099352941078846004 \pm 5 \cdot 10^{-10}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -0.09462920 \pm 1.5 \cdot 10^{-6} \) \(a_{3}= +1.58605341 \pm 1.4 \cdot 10^{-6} \)
\(a_{4}= -0.99104532 \pm 1.7 \cdot 10^{-6} \) \(a_{5}= +0.13251469 \pm 1.3 \cdot 10^{-6} \) \(a_{6}= -0.15008696 \pm 1.7 \cdot 10^{-6} \)
\(a_{7}= +1.85802001 \pm 1.2 \cdot 10^{-6} \) \(a_{8}= +0.18841102 \pm 1.7 \cdot 10^{-6} \) \(a_{9}= +1.51556544 \pm 1.3 \cdot 10^{-6} \)
\(a_{10}= -0.01253976 \pm 1.6 \cdot 10^{-6} \) \(a_{11}= +1.40709082 \pm 1.2 \cdot 10^{-6} \) \(a_{12}= -1.57185081 \pm 2.0 \cdot 10^{-6} \)
\(a_{13}= -1.02802903 \pm 1.3 \cdot 10^{-6} \) \(a_{14}= -0.17582294 \pm 1.3 \cdot 10^{-6} \) \(a_{15}= +0.21017538 \pm 1.3 \cdot 10^{-6} \)
\(a_{16}= +0.97321613 \pm 1.5 \cdot 10^{-6} \) \(a_{17}= -0.08189494 \pm 1.2 \cdot 10^{-6} \) \(a_{18}= -0.14341674 \pm 1.7 \cdot 10^{-6} \)
\(a_{19}= -0.38772651 \pm 1.3 \cdot 10^{-6} \) \(a_{20}= -0.13132807 \pm 1.6 \cdot 10^{-6} \) \(a_{21}= +2.94691898 \pm 1.3 \cdot 10^{-6} \)
\(a_{22}= -0.13315187 \pm 1.3 \cdot 10^{-6} \) \(a_{23}= -0.91583817 \pm 1.2 \cdot 10^{-6} \) \(a_{24}= +0.29882993 \pm 2.1 \cdot 10^{-6} \)
\(a_{25}= -0.98243986 \pm 1.2 \cdot 10^{-6} \) \(a_{26}= +0.09728156 \pm 1.3 \cdot 10^{-6} \) \(a_{27}= +0.81771432 \pm 1.1 \cdot 10^{-6} \)
\(a_{28}= -1.84138203 \pm 1.3 \cdot 10^{-6} \) \(a_{29}= +1.01667504 \pm 1.2 \cdot 10^{-6} \) \(a_{30}= -0.01988873 \pm 1.7 \cdot 10^{-6} \)
\(a_{31}= +0.17960530 \pm 1.0 \cdot 10^{-8} \) \(a_{32}= -0.28050568 \pm 1.7 \cdot 10^{-6} \) \(a_{33}= +2.23172121 \pm 1.3 \cdot 10^{-6} \)
\(a_{34}= +0.00774965 \pm 1.6 \cdot 10^{-6} \) \(a_{35}= +0.24621495 \pm 1.1 \cdot 10^{-6} \) \(a_{36}= -1.50199402 \pm 1.8 \cdot 10^{-6} \)
\(a_{37}= +0.62519855 \pm 1.1 \cdot 10^{-6} \) \(a_{38}= +0.03669025 \pm 1.6 \cdot 10^{-6} \) \(a_{39}= -1.63050895 \pm 1.3 \cdot 10^{-6} \)
\(a_{40}= +0.02496723 \pm 1.7 \cdot 10^{-6} \) \(a_{41}= -0.44574978 \pm 1.1 \cdot 10^{-6} \) \(a_{42}= -0.27886457 \pm 1.5 \cdot 10^{-6} \)
\(a_{43}= -0.90662915 \pm 1.1 \cdot 10^{-6} \) \(a_{44}= -1.39449077 \pm 1.3 \cdot 10^{-6} \) \(a_{45}= +0.20083469 \pm 1.2 \cdot 10^{-6} \)
\(a_{46}= +0.08666503 \pm 1.1 \cdot 10^{-6} \) \(a_{47}= -0.48417268 \pm 1.1 \cdot 10^{-6} \) \(a_{48}= +1.54357277 \pm 1.9 \cdot 10^{-6} \)
\(a_{49}= +2.45223835 \pm 1.2 \cdot 10^{-6} \) \(a_{50}= +0.09296749 \pm 1.5 \cdot 10^{-6} \) \(a_{51}= -0.12988976 \pm 1.3 \cdot 10^{-6} \)
\(a_{52}= +1.01882335 \pm 1.3 \cdot 10^{-6} \) \(a_{53}= -0.64262670 \pm 1.2 \cdot 10^{-6} \) \(a_{54}= -0.07737965 \pm 1.5 \cdot 10^{-6} \)
\(a_{55}= +0.18646021 \pm 1.3 \cdot 10^{-6} \) \(a_{56}= +0.35007144 \pm 1.3 \cdot 10^{-6} \) \(a_{57}= -0.61495495 \pm 1.3 \cdot 10^{-6} \)
\(a_{58}= -0.09620714 \pm 1.4 \cdot 10^{-6} \) \(a_{59}= +0.41963749 \pm 1.3 \cdot 10^{-6} \) \(a_{60}= -0.20829333 \pm 2.0 \cdot 10^{-6} \)

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