Properties

Level $8$
Weight $0$
Character 8.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 8 = 2^{3} \)
Weight: \( 0 \)
Character: 8.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 10.6817988431 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=-1.109314263\) \(a_{4}=+0.000000000\) \(a_{5}=-1.549312826\)
\(a_{6}=+0.000000000\) \(a_{7}=-1.117411695\) \(a_{8}=+0.000000000\) \(a_{9}=+0.230578134\) \(a_{10}=+0.000000000\)
\(a_{11}=-1.026929770\) \(a_{12}=+0.000000000\) \(a_{13}=-1.225088317\) \(a_{14}=+0.000000000\) \(a_{15}=+1.718674815\)
\(a_{16}=+0.000000000\) \(a_{17}=+0.309810431\) \(a_{18}=+0.000000000\) \(a_{19}=+0.887526107\) \(a_{20}=+0.000000000\)
\(a_{21}=+1.239560731\) \(a_{22}=+0.000000000\) \(a_{23}=+0.244580003\) \(a_{24}=+0.000000000\) \(a_{25}=+1.400370228\)
\(a_{26}=+0.000000000\) \(a_{27}=+0.853530634\) \(a_{28}=+0.000000000\) \(a_{29}=-1.082468547\) \(a_{30}=+0.000000000\)
\(a_{31}=-0.784519680\) \(a_{32}=+0.000000000\) \(a_{33}=+1.139186638\) \(a_{34}=+0.000000000\) \(a_{35}=+1.731215743\)
\(a_{36}=+0.000000000\) \(a_{37}=-1.810535260\) \(a_{38}=+0.000000000\) \(a_{39}=+1.358951426\) \(a_{40}=+0.000000000\)
\(a_{41}=-0.973600011\) \(a_{42}=+0.000000000\) \(a_{43}=-0.467066179\) \(a_{44}=+0.000000000\) \(a_{45}=-0.359026192\)
\(a_{46}=+0.000000000\) \(a_{47}=+0.954205155\) \(a_{48}=+0.000000000\) \(a_{49}=+0.234406065\) \(a_{50}=+0.000000000\)
\(a_{51}=-0.380839215\) \(a_{52}=+0.000000000\)

Showing all 52 available coefficients

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