Properties

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

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Maass form invariants

Level: \( 8 = 2^{3} \)
Weight: \( 0 \)
Character: 8.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 4.36801954023 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=-1.375694020\) \(a_{4}=+0.000000000\) \(a_{5}=+0.214215674\)
\(a_{6}=+0.000000000\) \(a_{7}=-1.431673235\) \(a_{8}=+0.000000000\) \(a_{9}=+0.892534037\) \(a_{10}=+0.000000000\)
\(a_{11}=+0.078523292\) \(a_{12}=+0.000000000\) \(a_{13}=-0.019320749\) \(a_{14}=+0.000000000\) \(a_{15}=-0.294695221\)
\(a_{16}=+0.000000000\) \(a_{17}=-0.944756827\) \(a_{18}=+0.000000000\) \(a_{19}=+0.479745161\) \(a_{20}=+0.000000000\)
\(a_{21}=+1.969544308\) \(a_{22}=+0.000000000\) \(a_{23}=-0.930387795\) \(a_{24}=+0.000000000\) \(a_{25}=-0.954111645\)
\(a_{26}=+0.000000000\) \(a_{27}=+0.147840282\) \(a_{28}=+0.000000000\) \(a_{29}=-0.656149062\) \(a_{30}=+0.000000000\)
\(a_{31}=+0.964290240\) \(a_{32}=+0.000000000\) \(a_{33}=-0.108024023\) \(a_{34}=+0.000000000\) \(a_{35}=-0.306686846\)
\(a_{36}=+0.000000000\) \(a_{37}=+1.731927440\) \(a_{38}=+0.000000000\) \(a_{39}=+0.026579439\) \(a_{40}=+0.000000000\)
\(a_{41}=-1.479287000\) \(a_{42}=+0.000000000\) \(a_{43}=-1.100010000\) \(a_{44}=+0.000000000\) \(a_{45}=+0.191194780\)
\(a_{46}=+0.000000000\) \(a_{47}=-0.144800007\) \(a_{48}=+0.000000000\) \(a_{49}=+1.049688252\) \(a_{50}=+0.000000000\)
\(a_{51}=+1.299696318\) \(a_{52}=+0.000000000\) \(a_{53}=-0.639999390\) \(a_{54}=+0.000000000\) \(a_{55}=+0.016820920\)
\(a_{56}=+0.000000000\) \(a_{57}=-0.659982550\) \(a_{58}=+0.000000000\)

Showing all 58 available coefficients

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