Properties

Label 31.113
Level $31$
Weight $0$
Character 31.1
Symmetry odd
\(R\) 7.082315
Fricke sign $-1$

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Maass form invariants

Level: \( 31 \)
Weight: \( 0 \)
Character: 31.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \(7.08231598469276597683409060847 \pm 4 \cdot 10^{-9}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -1.37324925 \pm 9.0 \cdot 10^{-5} \) \(a_{3}= +0.01009749 \pm 8.1 \cdot 10^{-5} \)
\(a_{4}= +0.88581350 \pm 9.9 \cdot 10^{-5} \) \(a_{5}= -0.97936413 \pm 7.5 \cdot 10^{-5} \) \(a_{6}= -0.01386638 \pm 1.0 \cdot 10^{-4} \)
\(a_{7}= +1.86198482 \pm 7.4 \cdot 10^{-5} \) \(a_{8}= +0.15680652 \pm 1.0 \cdot 10^{-4} \) \(a_{9}= -0.99989804 \pm 7.7 \cdot 10^{-5} \)
\(a_{10}= +1.34491105 \pm 9.2 \cdot 10^{-5} \) \(a_{11}= +0.86129688 \pm 7.4 \cdot 10^{-5} \) \(a_{12}= +0.00894450 \pm 1.1 \cdot 10^{-4} \)
\(a_{13}= -0.60628719 \pm 7.7 \cdot 10^{-5} \) \(a_{14}= -2.55696925 \pm 7.6 \cdot 10^{-5} \) \(a_{15}= -0.00988912 \pm 7.8 \cdot 10^{-5} \)
\(a_{16}= -1.10114794 \pm 9.1 \cdot 10^{-5} \) \(a_{17}= -0.84860579 \pm 7.0 \cdot 10^{-5} \) \(a_{18}= +1.37310923 \pm 9.9 \cdot 10^{-5} \)
\(a_{19}= -0.29095950 \pm 7.8 \cdot 10^{-5} \) \(a_{20}= -0.86753396 \pm 9.5 \cdot 10^{-5} \) \(a_{21}= +0.01880138 \pm 7.9 \cdot 10^{-5} \)
\(a_{22}= -1.18277529 \pm 8.0 \cdot 10^{-5} \) \(a_{23}= +0.27506452 \pm 7.1 \cdot 10^{-5} \) \(a_{24}= +0.00158335 \pm 1.2 \cdot 10^{-4} \)
\(a_{25}= -0.04084591 \pm 7.1 \cdot 10^{-5} \) \(a_{26}= +0.83258343 \pm 7.8 \cdot 10^{-5} \) \(a_{27}= -0.02019396 \pm 6.8 \cdot 10^{-5} \)
\(a_{28}= +1.64937129 \pm 7.9 \cdot 10^{-5} \) \(a_{29}= -0.59976900 \pm 7.0 \cdot 10^{-5} \) \(a_{30}= +0.01358023 \pm 1.0 \cdot 10^{-4} \)
\(a_{31}= +0.17960530 \pm 1.0 \cdot 10^{-8} \) \(a_{32}= +1.35534406 \pm 9.8 \cdot 10^{-5} \) \(a_{33}= +0.00869694 \pm 7.9 \cdot 10^{-5} \)
\(a_{34}= +1.16534727 \pm 9.6 \cdot 10^{-5} \) \(a_{35}= -1.82356113 \pm 6.8 \cdot 10^{-5} \) \(a_{36}= -0.88572318 \pm 1.0 \cdot 10^{-4} \)
\(a_{37}= +1.56700577 \pm 6.8 \cdot 10^{-5} \) \(a_{38}= +0.39955992 \pm 9.4 \cdot 10^{-5} \) \(a_{39}= -0.00612198 \pm 7.5 \cdot 10^{-5} \)
\(a_{40}= -0.15357069 \pm 9.9 \cdot 10^{-5} \) \(a_{41}= -1.34140449 \pm 6.7 \cdot 10^{-5} \) \(a_{42}= -0.02581898 \pm 9.2 \cdot 10^{-5} \)
\(a_{43}= +0.72402159 \pm 6.4 \cdot 10^{-5} \) \(a_{44}= +0.76294840 \pm 7.8 \cdot 10^{-5} \) \(a_{45}= +0.97926427 \pm 7.5 \cdot 10^{-5} \)
\(a_{46}= -0.37773215 \pm 6.8 \cdot 10^{-5} \) \(a_{47}= +1.53229957 \pm 6.5 \cdot 10^{-5} \) \(a_{48}= -0.01111884 \pm 1.1 \cdot 10^{-4} \)
\(a_{49}= +2.46698745 \pm 7.0 \cdot 10^{-5} \) \(a_{50}= +0.05609161 \pm 9.0 \cdot 10^{-5} \) \(a_{51}= -0.00856879 \pm 8.0 \cdot 10^{-5} \)
\(a_{52}= -0.53705738 \pm 7.9 \cdot 10^{-5} \) \(a_{53}= -1.11528091 \pm 7.0 \cdot 10^{-5} \) \(a_{54}= +0.02773134 \pm 8.9 \cdot 10^{-5} \)
\(a_{55}= -0.84352327 \pm 7.9 \cdot 10^{-5} \) \(a_{56}= +0.29197137 \pm 7.6 \cdot 10^{-5} \) \(a_{57}= -0.00293796 \pm 7.6 \cdot 10^{-5} \)
\(a_{58}= +0.82363232 \pm 8.1 \cdot 10^{-5} \) \(a_{59}= -1.10896578 \pm 7.9 \cdot 10^{-5} \) \(a_{60}= -0.00875992 \pm 1.1 \cdot 10^{-4} \)

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