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: \( 3.24997696354 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=+1.214060411\) \(a_{4}=+0.000000000\) \(a_{5}=-0.490696037\)
\(a_{6}=+0.000000000\) \(a_{7}=-0.090531564\) \(a_{8}=+0.000000000\) \(a_{9}=+0.473942682\) \(a_{10}=+0.000000000\)
\(a_{11}=+0.778637099\) \(a_{12}=+0.000000000\) \(a_{13}=-1.431060843\) \(a_{14}=+0.000000000\) \(a_{15}=-0.595734632\)
\(a_{16}=+0.000000000\) \(a_{17}=+1.515104410\) \(a_{18}=+0.000000000\) \(a_{19}=-0.022395234\) \(a_{20}=+0.000000000\)
\(a_{21}=-0.109910787\) \(a_{22}=+0.000000000\) \(a_{23}=+0.310276740\) \(a_{24}=+0.000000000\) \(a_{25}=-0.759217400\)
\(a_{26}=+0.000000000\) \(a_{27}=-0.638665364\) \(a_{28}=+0.000000000\) \(a_{29}=-0.423216000\) \(a_{30}=+0.000000000\)
\(a_{31}=+1.262128994\) \(a_{32}=+0.000000000\) \(a_{33}=+0.945312476\) \(a_{34}=+0.000000000\) \(a_{35}=+0.044423479\)
\(a_{36}=+0.000000000\) \(a_{37}=-0.132309999\) \(a_{38}=+0.000000000\) \(a_{39}=-1.737394315\) \(a_{40}=+0.000000000\)
\(a_{41}=+0.405998230\) \(a_{42}=+0.000000000\)

Showing all 42 available coefficients

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