Properties

Label 31.80
Level $31$
Weight $0$
Character 31.1
Symmetry even
\(R\) 6.024011
Fricke sign $-1$

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 31 \)
Weight: \( 0 \)
Character: 31.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \(6.0240118248414898558027007829 \pm 3 \cdot 10^{-9}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -0.32033624 \pm 5.8 \cdot 10^{-7} \) \(a_{3}= +0.64761801 \pm 5.2 \cdot 10^{-7} \)
\(a_{4}= -0.89738470 \pm 5.8 \cdot 10^{-7} \) \(a_{5}= +0.23449548 \pm 5.0 \cdot 10^{-7} \) \(a_{6}= -0.20745552 \pm 5.8 \cdot 10^{-7} \)
\(a_{7}= +0.30076129 \pm 5.0 \cdot 10^{-7} \) \(a_{8}= +0.60780107 \pm 5.7 \cdot 10^{-7} \) \(a_{9}= -0.58059091 \pm 5.0 \cdot 10^{-7} \)
\(a_{10}= -0.07511740 \pm 4.8 \cdot 10^{-7} \) \(a_{11}= +1.01511087 \pm 5.0 \cdot 10^{-7} \) \(a_{12}= -0.58116249 \pm 5.5 \cdot 10^{-7} \)
\(a_{13}= +0.49529703 \pm 4.0 \cdot 10^{-7} \) \(a_{14}= -0.09634474 \pm 6.8 \cdot 10^{-7} \) \(a_{15}= +0.15186350 \pm 5.3 \cdot 10^{-7} \)
\(a_{16}= +0.70268399 \pm 6.0 \cdot 10^{-7} \) \(a_{17}= -1.05470006 \pm 4.7 \cdot 10^{-7} \) \(a_{18}= +0.18598431 \pm 4.4 \cdot 10^{-7} \)
\(a_{19}= -1.50491162 \pm 4.5 \cdot 10^{-7} \) \(a_{20}= -0.21043266 \pm 5.1 \cdot 10^{-7} \) \(a_{21}= +0.19477843 \pm 5.1 \cdot 10^{-7} \)
\(a_{22}= -0.32517679 \pm 5.9 \cdot 10^{-7} \) \(a_{23}= +0.34042850 \pm 4.0 \cdot 10^{-7} \) \(a_{24}= +0.39362292 \pm 6.0 \cdot 10^{-7} \)
\(a_{25}= -0.94501187 \pm 5.3 \cdot 10^{-7} \) \(a_{26}= -0.15866159 \pm 4.5 \cdot 10^{-7} \) \(a_{27}= -1.02361914 \pm 5.1 \cdot 10^{-7} \)
\(a_{28}= -0.26989858 \pm 7.3 \cdot 10^{-7} \) \(a_{29}= -1.66590041 \pm 4.8 \cdot 10^{-7} \) \(a_{30}= -0.04864738 \pm 5.4 \cdot 10^{-7} \)
\(a_{31}= +0.17960530 \pm 1.0 \cdot 10^{-8} \) \(a_{32}= -0.83289622 \pm 5.8 \cdot 10^{-7} \) \(a_{33}= +0.65740408 \pm 5.6 \cdot 10^{-7} \)
\(a_{34}= +0.33785865 \pm 5.0 \cdot 10^{-7} \) \(a_{35}= +0.07052716 \pm 5.2 \cdot 10^{-7} \) \(a_{36}= +0.52101340 \pm 4.4 \cdot 10^{-7} \)
\(a_{37}= -0.52259026 \pm 5.0 \cdot 10^{-7} \) \(a_{38}= +0.48207772 \pm 5.9 \cdot 10^{-7} \) \(a_{39}= +0.32076328 \pm 5.0 \cdot 10^{-7} \)
\(a_{40}= +0.14252660 \pm 4.7 \cdot 10^{-7} \) \(a_{41}= -0.51952373 \pm 3.8 \cdot 10^{-7} \) \(a_{42}= -0.06239459 \pm 6.7 \cdot 10^{-7} \)
\(a_{43}= +1.36911536 \pm 5.0 \cdot 10^{-7} \) \(a_{44}= -0.91094496 \pm 6.2 \cdot 10^{-7} \) \(a_{45}= -0.13614595 \pm 5.1 \cdot 10^{-7} \)
\(a_{46}= -0.10905159 \pm 5.0 \cdot 10^{-7} \) \(a_{47}= -1.18503146 \pm 4.4 \cdot 10^{-7} \) \(a_{48}= +0.45507081 \pm 5.5 \cdot 10^{-7} \)
\(a_{49}= -0.90954264 \pm 4.4 \cdot 10^{-7} \) \(a_{50}= +0.30272155 \pm 5.0 \cdot 10^{-7} \) \(a_{51}= -0.68304275 \pm 4.5 \cdot 10^{-7} \)
\(a_{52}= -0.44447198 \pm 4.4 \cdot 10^{-7} \) \(a_{53}= +0.64134326 \pm 5.0 \cdot 10^{-7} \) \(a_{54}= +0.32790230 \pm 5.5 \cdot 10^{-7} \)
\(a_{55}= +0.23803891 \pm 5.2 \cdot 10^{-7} \) \(a_{56}= +0.18280304 \pm 7.5 \cdot 10^{-7} \) \(a_{57}= -0.97460787 \pm 4.2 \cdot 10^{-7} \)
\(a_{58}= +0.53364827 \pm 5.9 \cdot 10^{-7} \) \(a_{59}= -0.67880345 \pm 4.0 \cdot 10^{-7} \) \(a_{60}= -0.13627998 \pm 5.1 \cdot 10^{-7} \)

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