Properties

Label 31.3
Level $31$
Weight $0$
Character 31.1
Symmetry odd
\(R\) 1.343010
Fricke sign $-1$

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Maass form invariants

Level: \( 31 \)
Weight: \( 0 \)
Character: 31.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \(1.34301045897290777549784873471 \pm 2 \cdot 10^{-10}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -1.82635852 \pm 1.2 \cdot 10^{-7} \) \(a_{3}= +1.17147430 \pm 1.1 \cdot 10^{-7} \)
\(a_{4}= +2.33558545 \pm 1.3 \cdot 10^{-7} \) \(a_{5}= +0.88276856 \pm 1.0 \cdot 10^{-7} \) \(a_{6}= -2.13953207 \pm 1.4 \cdot 10^{-7} \)
\(a_{7}= +0.08502050 \pm 1.0 \cdot 10^{-7} \) \(a_{8}= -2.43925787 \pm 1.4 \cdot 10^{-7} \) \(a_{9}= +0.37235204 \pm 1.0 \cdot 10^{-7} \)
\(a_{10}= -1.61225188 \pm 1.2 \cdot 10^{-7} \) \(a_{11}= +0.47974902 \pm 1.0 \cdot 10^{-7} \) \(a_{12}= +2.73607834 \pm 1.6 \cdot 10^{-7} \)
\(a_{13}= -0.48034161 \pm 1.0 \cdot 10^{-7} \) \(a_{14}= -0.15527792 \pm 1.0 \cdot 10^{-7} \) \(a_{15}= +1.03414068 \pm 1.0 \cdot 10^{-7} \)
\(a_{16}= +2.11937395 \pm 1.2 \cdot 10^{-7} \) \(a_{17}= -1.88973928 \pm 9.7 \cdot 10^{-8} \) \(a_{18}= -0.68004832 \pm 1.3 \cdot 10^{-7} \)
\(a_{19}= +0.57022534 \pm 1.0 \cdot 10^{-7} \) \(a_{20}= +2.06178141 \pm 1.3 \cdot 10^{-7} \) \(a_{21}= +0.09959933 \pm 1.1 \cdot 10^{-7} \)
\(a_{22}= -0.87619372 \pm 1.1 \cdot 10^{-7} \) \(a_{23}= -0.28272726 \pm 9.8 \cdot 10^{-8} \) \(a_{24}= -2.85752791 \pm 1.7 \cdot 10^{-7} \)
\(a_{25}= -0.22071967 \pm 9.9 \cdot 10^{-8} \) \(a_{26}= +0.87727599 \pm 1.0 \cdot 10^{-7} \) \(a_{27}= -0.73527346 \pm 9.4 \cdot 10^{-8} \)
\(a_{28}= +0.19857265 \pm 1.1 \cdot 10^{-7} \) \(a_{29}= +1.06745270 \pm 9.7 \cdot 10^{-8} \) \(a_{30}= -1.88871165 \pm 1.4 \cdot 10^{-7} \)
\(a_{31}= +0.17960530 \pm 1.0 \cdot 10^{-8} \) \(a_{32}= -1.43147881 \pm 1.3 \cdot 10^{-7} \) \(a_{33}= +0.56201365 \pm 1.0 \cdot 10^{-7} \)
\(a_{34}= +3.45134143 \pm 1.3 \cdot 10^{-7} \) \(a_{35}= +0.07505343 \pm 9.5 \cdot 10^{-8} \) \(a_{36}= +0.86966001 \pm 1.4 \cdot 10^{-7} \)
\(a_{37}= +0.96163327 \pm 9.4 \cdot 10^{-8} \) \(a_{38}= -1.04143591 \pm 1.3 \cdot 10^{-7} \) \(a_{39}= -0.56270785 \pm 1.0 \cdot 10^{-7} \)
\(a_{40}= -2.15330016 \pm 1.3 \cdot 10^{-7} \) \(a_{41}= -0.74921074 \pm 9.3 \cdot 10^{-8} \) \(a_{42}= -0.18190409 \pm 1.2 \cdot 10^{-7} \)
\(a_{43}= +0.20338915 \pm 8.9 \cdot 10^{-8} \) \(a_{44}= +1.12049484 \pm 1.0 \cdot 10^{-7} \) \(a_{45}= +0.32870067 \pm 1.0 \cdot 10^{-7} \)
\(a_{46}= +0.51636134 \pm 9.4 \cdot 10^{-8} \) \(a_{47}= -0.68206036 \pm 9.1 \cdot 10^{-8} \) \(a_{48}= +2.48279212 \pm 1.6 \cdot 10^{-7} \)
\(a_{49}= -0.99277151 \pm 9.8 \cdot 10^{-8} \) \(a_{50}= +0.40311325 \pm 1.2 \cdot 10^{-7} \) \(a_{51}= -2.21378100 \pm 1.1 \cdot 10^{-7} \)
\(a_{52}= -1.12187887 \pm 1.1 \cdot 10^{-7} \) \(a_{53}= +0.25787741 \pm 9.7 \cdot 10^{-8} \) \(a_{54}= +1.34287294 \pm 1.2 \cdot 10^{-7} \)
\(a_{55}= +0.42350735 \pm 1.1 \cdot 10^{-7} \) \(a_{56}= -0.20738693 \pm 1.0 \cdot 10^{-7} \) \(a_{57}= +0.66800433 \pm 1.0 \cdot 10^{-7} \)
\(a_{58}= -1.94955133 \pm 1.1 \cdot 10^{-7} \) \(a_{59}= +1.67030159 \pm 1.1 \cdot 10^{-7} \) \(a_{60}= +2.41532393 \pm 1.6 \cdot 10^{-7} \)

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