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: \( 4.94783167713 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=+1.526687812\) \(a_{4}=+0.000000000\) \(a_{5}=+0.748605236\)
\(a_{6}=+0.000000000\) \(a_{7}=+0.147674867\) \(a_{8}=+0.000000000\) \(a_{9}=+1.330775674\) \(a_{10}=+0.000000000\)
\(a_{11}=-1.538988733\) \(a_{12}=+0.000000000\) \(a_{13}=+0.001710237\) \(a_{14}=+0.000000000\) \(a_{15}=+1.142886490\)
\(a_{16}=+0.000000000\) \(a_{17}=+0.086271416\) \(a_{18}=+0.000000000\) \(a_{19}=-0.685272297\) \(a_{20}=+0.000000000\)
\(a_{21}=+0.225453419\) \(a_{22}=+0.000000000\) \(a_{23}=-0.558789910\) \(a_{24}=+0.000000000\) \(a_{25}=-0.439590200\)
\(a_{26}=+0.000000000\) \(a_{27}=+0.504991190\) \(a_{28}=+0.000000000\) \(a_{29}=+1.740748003\) \(a_{30}=+0.000000000\)
\(a_{31}=+0.204921000\) \(a_{32}=+0.000000000\) \(a_{33}=-2.349555340\) \(a_{34}=+0.000000000\) \(a_{35}=+0.110550178\)
\(a_{36}=+0.000000000\) \(a_{37}=+0.059700012\) \(a_{38}=+0.000000000\) \(a_{39}=+0.002610998\) \(a_{40}=+0.000000000\)
\(a_{41}=+1.188995361\) \(a_{42}=+0.000000000\) \(a_{43}=-1.250000000\) \(a_{44}=+0.000000000\) \(a_{45}=+0.996225638\)
\(a_{46}=+0.000000000\) \(a_{47}=+1.099609375\) \(a_{48}=+0.000000000\) \(a_{49}=-0.978192134\) \(a_{50}=+0.000000000\)
\(a_{51}=+0.131709519\) \(a_{52}=+0.000000000\) \(a_{53}=+0.000000000\) \(a_{54}=+0.000000000\) \(a_{55}=-1.152095024\)
\(a_{56}=+0.000000000\) \(a_{57}=-1.046196863\) \(a_{58}=+0.000000000\)

Showing all 58 available coefficients

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