Properties

Label 31.94
Level $31$
Weight $0$
Character 31.1
Symmetry even
\(R\) 6.538767
Fricke sign $+1$

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Maass form invariants

Level: \( 31 \)
Weight: \( 0 \)
Character: 31.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \(6.5387670955789320362867853802 \pm 2 \cdot 10^{-9}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +0.91316670 \pm 3.3 \cdot 10^{-7} \) \(a_{3}= +1.81100739 \pm 3.0 \cdot 10^{-7} \)
\(a_{4}= -0.16612657 \pm 3.4 \cdot 10^{-7} \) \(a_{5}= +1.81406943 \pm 2.9 \cdot 10^{-7} \) \(a_{6}= +1.65375165 \pm 3.4 \cdot 10^{-7} \)
\(a_{7}= +0.67324365 \pm 2.9 \cdot 10^{-7} \) \(a_{8}= -1.06486796 \pm 3.3 \cdot 10^{-7} \) \(a_{9}= +2.27974777 \pm 2.9 \cdot 10^{-7} \)
\(a_{10}= +1.65654780 \pm 2.8 \cdot 10^{-7} \) \(a_{11}= +0.54050176 \pm 2.9 \cdot 10^{-7} \) \(a_{12}= -0.30085645 \pm 3.2 \cdot 10^{-7} \)
\(a_{13}= -1.47693123 \pm 2.3 \cdot 10^{-7} \) \(a_{14}= +0.61478368 \pm 3.9 \cdot 10^{-7} \) \(a_{15}= +3.28529315 \pm 3.1 \cdot 10^{-7} \)
\(a_{16}= -0.80627539 \pm 3.5 \cdot 10^{-7} \) \(a_{17}= -0.60165769 \pm 2.7 \cdot 10^{-7} \) \(a_{18}= +2.08178975 \pm 2.5 \cdot 10^{-7} \)
\(a_{19}= -0.98589844 \pm 2.6 \cdot 10^{-7} \) \(a_{20}= -0.30136514 \pm 2.9 \cdot 10^{-7} \) \(a_{21}= +1.21924922 \pm 2.9 \cdot 10^{-7} \)
\(a_{22}= +0.49356821 \pm 3.4 \cdot 10^{-7} \) \(a_{23}= -0.07094194 \pm 2.3 \cdot 10^{-7} \) \(a_{24}= -1.92848374 \pm 3.5 \cdot 10^{-7} \)
\(a_{25}= +2.29084791 \pm 3.1 \cdot 10^{-7} \) \(a_{26}= -1.34868442 \pm 2.6 \cdot 10^{-7} \) \(a_{27}= +2.31763266 \pm 3.0 \cdot 10^{-7} \)
\(a_{28}= -0.11184366 \pm 4.2 \cdot 10^{-7} \) \(a_{29}= -0.00268686 \pm 2.8 \cdot 10^{-7} \) \(a_{30}= +3.00002031 \pm 3.1 \cdot 10^{-7} \)
\(a_{31}= -0.17960530 \pm 1.0 \cdot 10^{-8} \) \(a_{32}= +0.32860412 \pm 3.4 \cdot 10^{-7} \) \(a_{33}= +0.97885268 \pm 3.3 \cdot 10^{-7} \)
\(a_{34}= -0.54941376 \pm 2.9 \cdot 10^{-7} \) \(a_{35}= +1.22131072 \pm 3.0 \cdot 10^{-7} \) \(a_{36}= -0.37872669 \pm 2.5 \cdot 10^{-7} \)
\(a_{37}= +0.82214467 \pm 2.9 \cdot 10^{-7} \) \(a_{38}= -0.90028963 \pm 3.4 \cdot 10^{-7} \) \(a_{39}= -2.67473337 \pm 2.9 \cdot 10^{-7} \)
\(a_{40}= -1.93174441 \pm 2.7 \cdot 10^{-7} \) \(a_{41}= -0.29996719 \pm 2.2 \cdot 10^{-7} \) \(a_{42}= +1.11337779 \pm 3.9 \cdot 10^{-7} \)
\(a_{43}= +0.48922282 \pm 2.9 \cdot 10^{-7} \) \(a_{44}= -0.08979171 \pm 3.6 \cdot 10^{-7} \) \(a_{45}= +4.13562074 \pm 3.0 \cdot 10^{-7} \)
\(a_{46}= -0.06478182 \pm 2.9 \cdot 10^{-7} \) \(a_{47}= -0.68850955 \pm 2.5 \cdot 10^{-7} \) \(a_{48}= -1.46017068 \pm 3.2 \cdot 10^{-7} \)
\(a_{49}= -0.54674299 \pm 2.6 \cdot 10^{-7} \) \(a_{50}= +2.09192603 \pm 2.9 \cdot 10^{-7} \) \(a_{51}= -1.08960651 \pm 2.6 \cdot 10^{-7} \)
\(a_{52}= +0.24535753 \pm 2.6 \cdot 10^{-7} \) \(a_{53}= +0.58283668 \pm 2.9 \cdot 10^{-7} \) \(a_{54}= +2.11638497 \pm 3.2 \cdot 10^{-7} \)
\(a_{55}= +0.98050772 \pm 3.0 \cdot 10^{-7} \) \(a_{56}= -0.71691559 \pm 4.3 \cdot 10^{-7} \) \(a_{57}= -1.78546937 \pm 2.4 \cdot 10^{-7} \)
\(a_{58}= -0.00245355 \pm 3.4 \cdot 10^{-7} \) \(a_{59}= +0.40005175 \pm 2.3 \cdot 10^{-7} \) \(a_{60}= -0.54577450 \pm 2.9 \cdot 10^{-7} \)

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