Properties

Label 31.115
Level $31$
Weight $0$
Character 31.1
Symmetry odd
\(R\) 7.185997
Fricke sign $+1$

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Maass form invariants

Level: \( 31 \)
Weight: \( 0 \)
Character: 31.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \(7.18599729591329426429446385356 \pm 6 \cdot 10^{-9}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +0.41183639 \pm 1.5 \cdot 10^{-5} \) \(a_{3}= +0.90344191 \pm 1.4 \cdot 10^{-5} \)
\(a_{4}= -0.83039079 \pm 1.7 \cdot 10^{-5} \) \(a_{5}= +0.28773136 \pm 1.3 \cdot 10^{-5} \) \(a_{6}= +0.37207026 \pm 1.8 \cdot 10^{-5} \)
\(a_{7}= +0.64722930 \pm 1.3 \cdot 10^{-5} \) \(a_{8}= -0.75382153 \pm 1.8 \cdot 10^{-5} \) \(a_{9}= -0.18379271 \pm 1.3 \cdot 10^{-5} \)
\(a_{10}= +0.11849824 \pm 1.6 \cdot 10^{-5} \) \(a_{11}= -0.12700621 \pm 1.3 \cdot 10^{-5} \) \(a_{12}= -0.75020984 \pm 2.1 \cdot 10^{-5} \)
\(a_{13}= -0.83651664 \pm 1.3 \cdot 10^{-5} \) \(a_{14}= +0.26655258 \pm 1.3 \cdot 10^{-5} \) \(a_{15}= +0.25994857 \pm 1.3 \cdot 10^{-5} \)
\(a_{16}= +0.51993965 \pm 1.6 \cdot 10^{-5} \) \(a_{17}= -0.19944859 \pm 1.2 \cdot 10^{-5} \) \(a_{18}= -0.07569253 \pm 1.7 \cdot 10^{-5} \)
\(a_{19}= +0.51192900 \pm 1.3 \cdot 10^{-5} \) \(a_{20}= -0.23892947 \pm 1.6 \cdot 10^{-5} \) \(a_{21}= +0.58473408 \pm 1.4 \cdot 10^{-5} \)
\(a_{22}= -0.05230578 \pm 1.4 \cdot 10^{-5} \) \(a_{23}= -0.96526190 \pm 1.2 \cdot 10^{-5} \) \(a_{24}= -0.68103397 \pm 2.1 \cdot 10^{-5} \)
\(a_{25}= -0.91721067 \pm 1.2 \cdot 10^{-5} \) \(a_{26}= -0.34450799 \pm 1.3 \cdot 10^{-5} \) \(a_{27}= -1.06948795 \pm 1.2 \cdot 10^{-5} \)
\(a_{28}= -0.53745325 \pm 1.3 \cdot 10^{-5} \) \(a_{29}= +0.19651305 \pm 1.2 \cdot 10^{-5} \) \(a_{30}= +0.10705628 \pm 1.8 \cdot 10^{-5} \)
\(a_{31}= -0.17960530 \pm 1.0 \cdot 10^{-8} \) \(a_{32}= +0.96795160 \pm 1.7 \cdot 10^{-5} \) \(a_{33}= -0.11474273 \pm 1.3 \cdot 10^{-5} \)
\(a_{34}= -0.08214019 \pm 1.6 \cdot 10^{-5} \) \(a_{35}= +0.18622817 \pm 1.2 \cdot 10^{-5} \) \(a_{36}= +0.15261977 \pm 1.8 \cdot 10^{-5} \)
\(a_{37}= -1.52302944 \pm 1.1 \cdot 10^{-5} \) \(a_{38}= +0.21083099 \pm 1.6 \cdot 10^{-5} \) \(a_{39}= -0.75574419 \pm 1.3 \cdot 10^{-5} \)
\(a_{40}= -0.21689809 \pm 1.7 \cdot 10^{-5} \) \(a_{41}= -1.96922169 \pm 1.1 \cdot 10^{-5} \) \(a_{42}= +0.24081477 \pm 1.6 \cdot 10^{-5} \)
\(a_{43}= -0.56628371 \pm 1.1 \cdot 10^{-5} \) \(a_{44}= +0.10546479 \pm 1.3 \cdot 10^{-5} \) \(a_{45}= -0.05288293 \pm 1.3 \cdot 10^{-5} \)
\(a_{46}= -0.39752998 \pm 1.1 \cdot 10^{-5} \) \(a_{47}= +0.03769483 \pm 1.1 \cdot 10^{-5} \) \(a_{48}= +0.46973527 \pm 2.0 \cdot 10^{-5} \)
\(a_{49}= -0.58109423 \pm 1.2 \cdot 10^{-5} \) \(a_{50}= -0.37774073 \pm 1.5 \cdot 10^{-5} \) \(a_{51}= -0.18019022 \pm 1.4 \cdot 10^{-5} \)
\(a_{52}= +0.69463571 \pm 1.3 \cdot 10^{-5} \) \(a_{53}= +0.35604303 \pm 1.2 \cdot 10^{-5} \) \(a_{54}= -0.44045406 \pm 1.5 \cdot 10^{-5} \)
\(a_{55}= -0.03654367 \pm 1.4 \cdot 10^{-5} \) \(a_{56}= -0.48789538 \pm 1.3 \cdot 10^{-5} \) \(a_{57}= +0.46249811 \pm 1.3 \cdot 10^{-5} \)
\(a_{58}= +0.08093122 \pm 1.4 \cdot 10^{-5} \) \(a_{59}= +0.26390262 \pm 1.4 \cdot 10^{-5} \) \(a_{60}= -0.21585890 \pm 2.0 \cdot 10^{-5} \)

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