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: \( 8.21171118246 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=-0.265086792\) \(a_{4}=+0.000000000\) \(a_{5}=+0.358446209\)
\(a_{6}=+0.000000000\) \(a_{7}=+0.720079877\) \(a_{8}=+0.000000000\) \(a_{9}=-0.929728993\) \(a_{10}=+0.000000000\)
\(a_{11}=-1.842611144\) \(a_{12}=+0.000000000\) \(a_{13}=-0.238318454\) \(a_{14}=+0.000000000\) \(a_{15}=-0.095019356\)
\(a_{16}=+0.000000000\) \(a_{17}=-1.403145158\) \(a_{18}=+0.000000000\) \(a_{19}=-0.045482886\) \(a_{20}=+0.000000000\)
\(a_{21}=-0.190883665\) \(a_{22}=+0.000000000\) \(a_{23}=+1.239091737\) \(a_{24}=+0.000000000\) \(a_{25}=-0.871516315\)
\(a_{26}=+0.000000000\) \(a_{27}=+0.511545668\) \(a_{28}=+0.000000000\) \(a_{29}=-1.432943800\) \(a_{30}=+0.000000000\)
\(a_{31}=+0.246529900\) \(a_{32}=+0.000000000\) \(a_{33}=+0.488451877\) \(a_{34}=+0.000000000\) \(a_{35}=+0.258109902\)
\(a_{36}=+0.000000000\) \(a_{37}=+0.707809985\) \(a_{38}=+0.000000000\) \(a_{39}=+0.063175075\) \(a_{40}=+0.000000000\)
\(a_{41}=-1.013399959\) \(a_{42}=+0.000000000\) \(a_{43}=-0.593000412\) \(a_{44}=+0.000000000\) \(a_{45}=-0.333257833\)
\(a_{46}=+0.000000000\) \(a_{47}=+1.060058594\) \(a_{48}=+0.000000000\) \(a_{49}=-0.481484970\) \(a_{50}=+0.000000000\)
\(a_{51}=+0.371955249\) \(a_{52}=+0.000000000\) \(a_{53}=+1.400000000\) \(a_{54}=+0.000000000\) \(a_{55}=-0.660476979\)
\(a_{56}=+0.000000000\) \(a_{57}=+0.012056912\) \(a_{58}=+0.000000000\)

Showing all 58 available coefficients

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