Properties

Label 31.81
Level $31$
Weight $0$
Character 31.1
Symmetry odd
\(R\) 6.124111
Fricke sign $-1$

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Maass form invariants

Level: \( 31 \)
Weight: \( 0 \)
Character: 31.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \(6.12411113219776963127482139938 \pm 9 \cdot 10^{-10}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +1.94212887 \pm 1.6 \cdot 10^{-6} \) \(a_{3}= -1.20254193 \pm 1.4 \cdot 10^{-6} \)
\(a_{4}= +2.77186456 \pm 1.7 \cdot 10^{-6} \) \(a_{5}= +0.49875269 \pm 1.3 \cdot 10^{-6} \) \(a_{6}= -2.33549141 \pm 1.8 \cdot 10^{-6} \)
\(a_{7}= -0.29278735 \pm 1.3 \cdot 10^{-6} \) \(a_{8}= +3.44118932 \pm 1.8 \cdot 10^{-6} \) \(a_{9}= +0.44610710 \pm 1.3 \cdot 10^{-6} \)
\(a_{10}= +0.96864199 \pm 1.6 \cdot 10^{-6} \) \(a_{11}= +0.47838161 \pm 1.3 \cdot 10^{-6} \) \(a_{12}= -3.33328336 \pm 2.1 \cdot 10^{-6} \)
\(a_{13}= +1.21754187 \pm 1.3 \cdot 10^{-6} \) \(a_{14}= -0.56863076 \pm 1.3 \cdot 10^{-6} \) \(a_{15}= -0.59977102 \pm 1.4 \cdot 10^{-6} \)
\(a_{16}= +3.91136857 \pm 1.6 \cdot 10^{-6} \) \(a_{17}= +1.30147145 \pm 1.2 \cdot 10^{-6} \) \(a_{18}= +0.86639748 \pm 1.7 \cdot 10^{-6} \)
\(a_{19}= -0.63304503 \pm 1.4 \cdot 10^{-6} \) \(a_{20}= +1.38247489 \pm 1.7 \cdot 10^{-6} \) \(a_{21}= +0.35208906 \pm 1.4 \cdot 10^{-6} \)
\(a_{22}= +0.92907875 \pm 1.4 \cdot 10^{-6} \) \(a_{23}= +1.92443792 \pm 1.2 \cdot 10^{-6} \) \(a_{24}= -4.13817445 \pm 2.2 \cdot 10^{-6} \)
\(a_{25}= -0.75124576 \pm 1.2 \cdot 10^{-6} \) \(a_{26}= +2.36462323 \pm 1.4 \cdot 10^{-6} \) \(a_{27}= +0.66607944 \pm 1.2 \cdot 10^{-6} \)
\(a_{28}= -0.81156688 \pm 1.4 \cdot 10^{-6} \) \(a_{29}= -0.69847143 \pm 1.2 \cdot 10^{-6} \) \(a_{30}= -1.16483261 \pm 1.8 \cdot 10^{-6} \)
\(a_{31}= +0.17960530 \pm 1.0 \cdot 10^{-8} \) \(a_{32}= +4.15519251 \pm 1.7 \cdot 10^{-6} \) \(a_{33}= -0.57527395 \pm 1.4 \cdot 10^{-6} \)
\(a_{34}= +2.52762527 \pm 1.7 \cdot 10^{-6} \) \(a_{35}= -0.14602848 \pm 1.2 \cdot 10^{-6} \) \(a_{36}= +1.23654846 \pm 1.9 \cdot 10^{-6} \)
\(a_{37}= -1.48380780 \pm 1.2 \cdot 10^{-6} \) \(a_{38}= -1.22945504 \pm 1.6 \cdot 10^{-6} \) \(a_{39}= -1.46414516 \pm 1.3 \cdot 10^{-6} \)
\(a_{40}= +1.71630241 \pm 1.7 \cdot 10^{-6} \) \(a_{41}= -0.39792787 \pm 1.2 \cdot 10^{-6} \) \(a_{42}= +0.68380234 \pm 1.6 \cdot 10^{-6} \)
\(a_{43}= -1.25116614 \pm 1.1 \cdot 10^{-6} \) \(a_{44}= +1.32600904 \pm 1.4 \cdot 10^{-6} \) \(a_{45}= +0.22249711 \pm 1.3 \cdot 10^{-6} \)
\(a_{46}= +3.73750645 \pm 1.2 \cdot 10^{-6} \) \(a_{47}= +0.74238118 \pm 1.1 \cdot 10^{-6} \) \(a_{48}= -4.70358472 \pm 2.0 \cdot 10^{-6} \)
\(a_{49}= -0.91427557 \pm 1.2 \cdot 10^{-6} \) \(a_{50}= -1.45901608 \pm 1.6 \cdot 10^{-6} \) \(a_{51}= -1.56507399 \pm 1.4 \cdot 10^{-6} \)
\(a_{52}= +3.37486117 \pm 1.4 \cdot 10^{-6} \) \(a_{53}= -0.62990080 \pm 1.2 \cdot 10^{-6} \) \(a_{54}= +1.29361211 \pm 1.6 \cdot 10^{-6} \)
\(a_{55}= +0.23859411 \pm 1.4 \cdot 10^{-6} \) \(a_{56}= -1.00753670 \pm 1.3 \cdot 10^{-6} \) \(a_{57}= +0.76126320 \pm 1.3 \cdot 10^{-6} \)
\(a_{58}= -1.35652152 \pm 1.4 \cdot 10^{-6} \) \(a_{59}= +0.24912381 \pm 1.4 \cdot 10^{-6} \) \(a_{60}= -1.66248403 \pm 2.1 \cdot 10^{-6} \)

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