Properties

Label 31.21
Level $31$
Weight $0$
Character 31.1
Symmetry odd
\(R\) 3.371466
Fricke sign $+1$

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Maass form invariants

Level: \( 31 \)
Weight: \( 0 \)
Character: 31.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \(3.37146672686425279748201767124 \pm 3 \cdot 10^{-10}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -1.54411217 \pm 1.0 \cdot 10^{-5} \) \(a_{3}= +1.49181982 \pm 9.6 \cdot 10^{-6} \)
\(a_{4}= +1.38428238 \pm 1.1 \cdot 10^{-5} \) \(a_{5}= -0.37697919 \pm 8.9 \cdot 10^{-6} \) \(a_{6}= -2.30353713 \pm 1.2 \cdot 10^{-5} \)
\(a_{7}= -1.15719140 \pm 8.7 \cdot 10^{-6} \) \(a_{8}= -0.59337510 \pm 1.2 \cdot 10^{-5} \) \(a_{9}= +1.22552637 \pm 9.1 \cdot 10^{-6} \)
\(a_{10}= +0.58209815 \pm 1.0 \cdot 10^{-5} \) \(a_{11}= -1.57115854 \pm 8.7 \cdot 10^{-6} \) \(a_{12}= +2.06509989 \pm 1.4 \cdot 10^{-5} \)
\(a_{13}= -1.19388368 \pm 9.1 \cdot 10^{-6} \) \(a_{14}= +1.78683333 \pm 9.0 \cdot 10^{-6} \) \(a_{15}= -0.56238502 \pm 9.2 \cdot 10^{-6} \)
\(a_{16}= -0.46804467 \pm 1.0 \cdot 10^{-5} \) \(a_{17}= +0.72683435 \pm 8.3 \cdot 10^{-6} \) \(a_{18}= -1.89235017 \pm 1.1 \cdot 10^{-5} \)
\(a_{19}= -0.13826954 \pm 9.2 \cdot 10^{-6} \) \(a_{20}= -0.52184565 \pm 1.1 \cdot 10^{-5} \) \(a_{21}= -1.72632107 \pm 9.4 \cdot 10^{-6} \)
\(a_{22}= +2.42604501 \pm 9.5 \cdot 10^{-6} \) \(a_{23}= -0.29497333 \pm 8.4 \cdot 10^{-6} \) \(a_{24}= -0.88520873 \pm 1.4 \cdot 10^{-5} \)
\(a_{25}= -0.85788669 \pm 8.5 \cdot 10^{-6} \) \(a_{26}= +1.84349032 \pm 9.3 \cdot 10^{-6} \) \(a_{27}= +0.33644470 \pm 8.0 \cdot 10^{-6} \)
\(a_{28}= -1.60187967 \pm 9.4 \cdot 10^{-6} \) \(a_{29}= +1.67909844 \pm 8.3 \cdot 10^{-6} \) \(a_{30}= +0.86838556 \pm 1.2 \cdot 10^{-5} \)
\(a_{31}= -0.17960530 \pm 1.0 \cdot 10^{-8} \) \(a_{32}= +1.31608857 \pm 1.1 \cdot 10^{-5} \) \(a_{33}= -2.34388544 \pm 9.3 \cdot 10^{-6} \)
\(a_{34}= -1.12231377 \pm 1.1 \cdot 10^{-5} \) \(a_{35}= +0.43623708 \pm 8.1 \cdot 10^{-6} \) \(a_{36}= +1.69647456 \pm 1.2 \cdot 10^{-5} \)
\(a_{37}= -1.52144422 \pm 8.0 \cdot 10^{-6} \) \(a_{38}= +0.21350368 \pm 1.1 \cdot 10^{-5} \) \(a_{39}= -1.78105934 \pm 8.9 \cdot 10^{-6} \)
\(a_{40}= +0.22369006 \pm 1.1 \cdot 10^{-5} \) \(a_{41}= +1.02807692 \pm 7.9 \cdot 10^{-6} \) \(a_{42}= +2.66563336 \pm 1.0 \cdot 10^{-5} \)
\(a_{43}= +1.18304991 \pm 7.6 \cdot 10^{-6} \) \(a_{44}= -2.17492708 \pm 9.3 \cdot 10^{-6} \) \(a_{45}= -0.46199793 \pm 8.8 \cdot 10^{-6} \)
\(a_{46}= +0.45547191 \pm 8.0 \cdot 10^{-6} \) \(a_{47}= -0.32180536 \pm 7.8 \cdot 10^{-6} \) \(a_{48}= -0.69823832 \pm 1.3 \cdot 10^{-5} \)
\(a_{49}= +0.33909195 \pm 8.3 \cdot 10^{-6} \) \(a_{50}= +1.32467328 \pm 1.0 \cdot 10^{-5} \) \(a_{51}= +1.08430589 \pm 9.5 \cdot 10^{-6} \)
\(a_{52}= -1.65267215 \pm 9.4 \cdot 10^{-6} \) \(a_{53}= +0.05937141 \pm 8.3 \cdot 10^{-6} \) \(a_{54}= -0.51950836 \pm 1.0 \cdot 10^{-5} \)
\(a_{55}= +0.59229407 \pm 9.4 \cdot 10^{-6} \) \(a_{56}= +0.68664856 \pm 9.0 \cdot 10^{-6} \) \(a_{57}= -0.20627324 \pm 9.0 \cdot 10^{-6} \)
\(a_{58}= -2.59271632 \pm 9.7 \cdot 10^{-6} \) \(a_{59}= -0.49552876 \pm 9.4 \cdot 10^{-6} \) \(a_{60}= -0.77849968 \pm 1.3 \cdot 10^{-5} \)

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