Properties

Label 31.9
Level $31$
Weight $0$
Character 31.1
Symmetry odd
\(R\) 2.280685
Fricke sign $+1$

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Maass form invariants

Level: \( 31 \)
Weight: \( 0 \)
Character: 31.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \(2.2806857382355253830551205564 \pm 4 \cdot 10^{-10}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -0.83926043 \pm 1.4 \cdot 10^{-6} \) \(a_{3}= +0.51575128 \pm 1.3 \cdot 10^{-6} \)
\(a_{4}= -0.29564193 \pm 1.6 \cdot 10^{-6} \) \(a_{5}= -1.53687913 \pm 1.2 \cdot 10^{-6} \) \(a_{6}= -0.43284964 \pm 1.6 \cdot 10^{-6} \)
\(a_{7}= -0.22386340 \pm 1.2 \cdot 10^{-6} \) \(a_{8}= +1.08738100 \pm 1.6 \cdot 10^{-6} \) \(a_{9}= -0.73400062 \pm 1.2 \cdot 10^{-6} \)
\(a_{10}= +1.28984184 \pm 1.5 \cdot 10^{-6} \) \(a_{11}= +1.73696830 \pm 1.2 \cdot 10^{-6} \) \(a_{12}= -0.15247770 \pm 1.9 \cdot 10^{-6} \)
\(a_{13}= -1.41986022 \pm 1.2 \cdot 10^{-6} \) \(a_{14}= +0.18787969 \pm 1.2 \cdot 10^{-6} \) \(a_{15}= -0.79264737 \pm 1.2 \cdot 10^{-6} \)
\(a_{16}= -0.61695392 \pm 1.4 \cdot 10^{-6} \) \(a_{17}= -0.29357228 \pm 1.1 \cdot 10^{-6} \) \(a_{18}= +0.61601768 \pm 1.6 \cdot 10^{-6} \)
\(a_{19}= -0.81892866 \pm 1.2 \cdot 10^{-6} \) \(a_{20}= +0.45436591 \pm 1.5 \cdot 10^{-6} \) \(a_{21}= -0.11545783 \pm 1.2 \cdot 10^{-6} \)
\(a_{22}= -1.45776877 \pm 1.3 \cdot 10^{-6} \) \(a_{23}= -0.01589541 \pm 1.1 \cdot 10^{-6} \) \(a_{24}= +0.56081814 \pm 2.0 \cdot 10^{-6} \)
\(a_{25}= +1.36199745 \pm 1.1 \cdot 10^{-6} \) \(a_{26}= +1.19163250 \pm 1.2 \cdot 10^{-6} \) \(a_{27}= -0.89431303 \pm 1.1 \cdot 10^{-6} \)
\(a_{28}= +0.06618341 \pm 1.2 \cdot 10^{-6} \) \(a_{29}= -0.64307468 \pm 1.1 \cdot 10^{-6} \) \(a_{30}= +0.66523757 \pm 1.6 \cdot 10^{-6} \)
\(a_{31}= -0.17960530 \pm 1.0 \cdot 10^{-8} \) \(a_{32}= -0.56959599 \pm 1.6 \cdot 10^{-6} \) \(a_{33}= +0.89584362 \pm 1.2 \cdot 10^{-6} \)
\(a_{34}= +0.24638360 \pm 1.5 \cdot 10^{-6} \) \(a_{35}= +0.34405098 \pm 1.1 \cdot 10^{-6} \) \(a_{36}= +0.21700136 \pm 1.7 \cdot 10^{-6} \)
\(a_{37}= -0.14559214 \pm 1.1 \cdot 10^{-6} \) \(a_{38}= +0.68729442 \pm 1.5 \cdot 10^{-6} \) \(a_{39}= -0.73229472 \pm 1.2 \cdot 10^{-6} \)
\(a_{40}= -1.67117317 \pm 1.6 \cdot 10^{-6} \) \(a_{41}= -0.51594193 \pm 1.0 \cdot 10^{-6} \) \(a_{42}= +0.09689919 \pm 1.4 \cdot 10^{-6} \)
\(a_{43}= +1.43130308 \pm 1.0 \cdot 10^{-6} \) \(a_{44}= -0.51352066 \pm 1.2 \cdot 10^{-6} \) \(a_{45}= +1.12807023 \pm 1.2 \cdot 10^{-6} \)
\(a_{46}= +0.01334039 \pm 1.1 \cdot 10^{-6} \) \(a_{47}= +1.00443573 \pm 1.0 \cdot 10^{-6} \) \(a_{48}= -0.31819477 \pm 1.8 \cdot 10^{-6} \)
\(a_{49}= -0.94988518 \pm 1.1 \cdot 10^{-6} \) \(a_{50}= -1.14307056 \pm 1.4 \cdot 10^{-6} \) \(a_{51}= -0.15141028 \pm 1.3 \cdot 10^{-6} \)
\(a_{52}= +0.41977021 \pm 1.2 \cdot 10^{-6} \) \(a_{53}= -0.15450433 \pm 1.1 \cdot 10^{-6} \) \(a_{54}= +0.75056154 \pm 1.4 \cdot 10^{-6} \)
\(a_{55}= -2.66951033 \pm 1.2 \cdot 10^{-6} \) \(a_{56}= -0.24342481 \pm 1.2 \cdot 10^{-6} \) \(a_{57}= -0.42236350 \pm 1.2 \cdot 10^{-6} \)
\(a_{58}= +0.53970713 \pm 1.3 \cdot 10^{-6} \) \(a_{59}= +0.83387642 \pm 1.2 \cdot 10^{-6} \) \(a_{60}= +0.23433980 \pm 1.9 \cdot 10^{-6} \)

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