Properties

Label 31.8
Level $31$
Weight $0$
Character 31.1
Symmetry odd
\(R\) 2.232710
Fricke sign $-1$

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Maass form invariants

Level: \( 31 \)
Weight: \( 0 \)
Character: 31.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \(2.23271071476013831655819950919 \pm 4 \cdot 10^{-10}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +0.47772563 \pm 1.2 \cdot 10^{-6} \) \(a_{3}= +1.52208905 \pm 1.0 \cdot 10^{-6} \)
\(a_{4}= -0.77177822 \pm 1.3 \cdot 10^{-6} \) \(a_{5}= +1.13086727 \pm 1.0 \cdot 10^{-6} \) \(a_{6}= +0.72714095 \pm 1.3 \cdot 10^{-6} \)
\(a_{7}= -0.47678657 \pm 9.9 \cdot 10^{-7} \) \(a_{8}= -0.84642387 \pm 1.3 \cdot 10^{-6} \) \(a_{9}= +1.31675508 \pm 1.0 \cdot 10^{-6} \)
\(a_{10}= +0.54024428 \pm 1.2 \cdot 10^{-6} \) \(a_{11}= -1.11163133 \pm 9.9 \cdot 10^{-7} \) \(a_{12}= -1.17471518 \pm 1.6 \cdot 10^{-6} \)
\(a_{13}= -1.15182149 \pm 1.0 \cdot 10^{-6} \) \(a_{14}= -0.22777316 \pm 1.0 \cdot 10^{-6} \) \(a_{15}= +1.72128069 \pm 1.0 \cdot 10^{-6} \)
\(a_{16}= +0.36741984 \pm 1.2 \cdot 10^{-6} \) \(a_{17}= +1.22186166 \pm 9.3 \cdot 10^{-7} \) \(a_{18}= +0.62904765 \pm 1.3 \cdot 10^{-6} \)
\(a_{19}= +0.74104456 \pm 1.0 \cdot 10^{-6} \) \(a_{20}= -0.87277873 \pm 1.2 \cdot 10^{-6} \) \(a_{21}= -0.72571161 \pm 1.0 \cdot 10^{-6} \)
\(a_{22}= -0.53105478 \pm 1.0 \cdot 10^{-6} \) \(a_{23}= +1.45152405 \pm 9.4 \cdot 10^{-7} \) \(a_{24}= -1.28833251 \pm 1.6 \cdot 10^{-6} \)
\(a_{25}= +0.27886078 \pm 9.6 \cdot 10^{-7} \) \(a_{26}= -0.55025465 \pm 1.0 \cdot 10^{-6} \) \(a_{27}= +0.48212944 \pm 9.1 \cdot 10^{-7} \)
\(a_{28}= +0.36797349 \pm 1.0 \cdot 10^{-6} \) \(a_{29}= -1.22124753 \pm 9.3 \cdot 10^{-7} \) \(a_{30}= +0.82229991 \pm 1.3 \cdot 10^{-6} \)
\(a_{31}= +0.17960530 \pm 1.0 \cdot 10^{-8} \) \(a_{32}= +1.02194975 \pm 1.3 \cdot 10^{-6} \) \(a_{33}= -1.69200188 \pm 1.0 \cdot 10^{-6} \)
\(a_{34}= +0.58371464 \pm 1.2 \cdot 10^{-6} \) \(a_{35}= -0.53918232 \pm 9.1 \cdot 10^{-7} \) \(a_{36}= -1.01624289 \pm 1.4 \cdot 10^{-6} \)
\(a_{37}= +1.26175515 \pm 9.1 \cdot 10^{-7} \) \(a_{38}= +0.35401598 \pm 1.2 \cdot 10^{-6} \) \(a_{39}= -1.75317489 \pm 1.0 \cdot 10^{-6} \)
\(a_{40}= -0.95719305 \pm 1.3 \cdot 10^{-6} \) \(a_{41}= -0.45152599 \pm 9.0 \cdot 10^{-7} \) \(a_{42}= -0.34669104 \pm 1.2 \cdot 10^{-6} \)
\(a_{43}= -0.48791433 \pm 8.6 \cdot 10^{-7} \) \(a_{44}= +0.85793285 \pm 1.0 \cdot 10^{-6} \) \(a_{45}= +1.48907522 \pm 1.0 \cdot 10^{-6} \)
\(a_{46}= +0.69343024 \pm 9.0 \cdot 10^{-7} \) \(a_{47}= +1.23004339 \pm 8.8 \cdot 10^{-7} \) \(a_{48}= +0.55924572 \pm 1.5 \cdot 10^{-6} \)
\(a_{49}= -0.77267457 \pm 9.4 \cdot 10^{-7} \) \(a_{50}= +0.13321894 \pm 1.2 \cdot 10^{-6} \) \(a_{51}= +1.85978226 \pm 1.0 \cdot 10^{-6} \)
\(a_{52}= +0.88895074 \pm 1.0 \cdot 10^{-6} \) \(a_{53}= -0.85925918 \pm 9.4 \cdot 10^{-7} \) \(a_{54}= +0.23032559 \pm 1.1 \cdot 10^{-6} \)
\(a_{55}= -1.25710749 \pm 1.0 \cdot 10^{-6} \) \(a_{56}= +0.40356353 \pm 1.0 \cdot 10^{-6} \) \(a_{57}= +1.12793581 \pm 1.0 \cdot 10^{-6} \)
\(a_{58}= -0.58342125 \pm 1.0 \cdot 10^{-6} \) \(a_{59}= -0.88134123 \pm 1.0 \cdot 10^{-6} \) \(a_{60}= -1.32844695 \pm 1.5 \cdot 10^{-6} \)

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