Properties

Label 31.39
Level $31$
Weight $0$
Character 31.1
Symmetry even
\(R\) 4.431402
Fricke sign $+1$

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Maass form invariants

Level: \( 31 \)
Weight: \( 0 \)
Character: 31.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \(4.43140273993212913402678292432 \pm 5 \cdot 10^{-10}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +0.16244726 \pm 4.9 \cdot 10^{-7} \) \(a_{3}= -1.84226247 \pm 4.4 \cdot 10^{-7} \)
\(a_{4}= -0.97361089 \pm 4.9 \cdot 10^{-7} \) \(a_{5}= -0.77206094 \pm 4.2 \cdot 10^{-7} \) \(a_{6}= -0.29927049 \pm 5.0 \cdot 10^{-7} \)
\(a_{7}= -0.24107916 \pm 4.3 \cdot 10^{-7} \) \(a_{8}= -0.32060768 \pm 4.8 \cdot 10^{-7} \) \(a_{9}= +2.39393099 \pm 4.2 \cdot 10^{-7} \)
\(a_{10}= -0.12541918 \pm 4.1 \cdot 10^{-7} \) \(a_{11}= -1.65546023 \pm 4.2 \cdot 10^{-7} \) \(a_{12}= +1.79364680 \pm 4.7 \cdot 10^{-7} \)
\(a_{13}= -1.21223782 \pm 3.4 \cdot 10^{-7} \) \(a_{14}= -0.03916265 \pm 5.8 \cdot 10^{-7} \) \(a_{15}= +1.42233889 \pm 4.5 \cdot 10^{-7} \)
\(a_{16}= +0.92152905 \pm 5.1 \cdot 10^{-7} \) \(a_{17}= -0.85657269 \pm 4.0 \cdot 10^{-7} \) \(a_{18}= +0.38888753 \pm 3.7 \cdot 10^{-7} \)
\(a_{19}= +0.85745397 \pm 3.9 \cdot 10^{-7} \) \(a_{20}= +0.75168694 \pm 4.3 \cdot 10^{-7} \) \(a_{21}= +0.44413109 \pm 4.3 \cdot 10^{-7} \)
\(a_{22}= -0.26892498 \pm 5.0 \cdot 10^{-7} \) \(a_{23}= +0.61582761 \pm 3.4 \cdot 10^{-7} \) \(a_{24}= +0.59064349 \pm 5.1 \cdot 10^{-7} \)
\(a_{25}= -0.40392191 \pm 4.5 \cdot 10^{-7} \) \(a_{26}= -0.19692471 \pm 3.8 \cdot 10^{-7} \) \(a_{27}= -2.56798675 \pm 4.4 \cdot 10^{-7} \)
\(a_{28}= +0.23471730 \pm 6.2 \cdot 10^{-7} \) \(a_{29}= -1.21365555 \pm 4.0 \cdot 10^{-7} \) \(a_{30}= +0.23105505 \pm 4.6 \cdot 10^{-7} \)
\(a_{31}= -0.17960530 \pm 1.0 \cdot 10^{-8} \) \(a_{32}= +0.47030755 \pm 4.9 \cdot 10^{-7} \) \(a_{33}= +3.04979224 \pm 4.8 \cdot 10^{-7} \)
\(a_{34}= -0.13914788 \pm 4.2 \cdot 10^{-7} \) \(a_{35}= +0.18612780 \pm 4.4 \cdot 10^{-7} \) \(a_{36}= -2.33075728 \pm 3.7 \cdot 10^{-7} \)
\(a_{37}= -0.89138613 \pm 4.2 \cdot 10^{-7} \) \(a_{38}= +0.13929105 \pm 5.0 \cdot 10^{-7} \) \(a_{39}= +2.23326024 \pm 4.3 \cdot 10^{-7} \)
\(a_{40}= +0.24752867 \pm 4.0 \cdot 10^{-7} \) \(a_{41}= +0.78819462 \pm 3.3 \cdot 10^{-7} \) \(a_{42}= +0.07214788 \pm 5.7 \cdot 10^{-7} \)
\(a_{43}= +0.08051649 \pm 4.3 \cdot 10^{-7} \) \(a_{44}= +1.61177410 \pm 5.3 \cdot 10^{-7} \) \(a_{45}= -1.84826061 \pm 4.3 \cdot 10^{-7} \)
\(a_{46}= +0.10003951 \pm 4.3 \cdot 10^{-7} \) \(a_{47}= -0.25982956 \pm 3.7 \cdot 10^{-7} \) \(a_{48}= -1.69769838 \pm 4.6 \cdot 10^{-7} \)
\(a_{49}= -0.94188084 \pm 3.8 \cdot 10^{-7} \) \(a_{50}= -0.06561601 \pm 4.2 \cdot 10^{-7} \) \(a_{51}= +1.57803171 \pm 3.8 \cdot 10^{-7} \)
\(a_{52}= +1.18024794 \pm 3.8 \cdot 10^{-7} \) \(a_{53}= -0.26963702 \pm 4.2 \cdot 10^{-7} \) \(a_{54}= -0.41716241 \pm 4.7 \cdot 10^{-7} \)
\(a_{55}= +1.27811618 \pm 4.4 \cdot 10^{-7} \) \(a_{56}= +0.07729183 \pm 6.3 \cdot 10^{-7} \) \(a_{57}= -1.57965526 \pm 3.5 \cdot 10^{-7} \)
\(a_{58}= -0.19715502 \pm 5.0 \cdot 10^{-7} \) \(a_{59}= +1.08480985 \pm 3.4 \cdot 10^{-7} \) \(a_{60}= -1.38480463 \pm 4.3 \cdot 10^{-7} \)

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