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: \( 7.69684780643 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=+1.879650317\) \(a_{4}=+0.000000000\) \(a_{5}=+0.528451057\)
\(a_{6}=+0.000000000\) \(a_{7}=-0.425932784\) \(a_{8}=+0.000000000\) \(a_{9}=+2.533085314\) \(a_{10}=+0.000000000\)
\(a_{11}=+0.166327141\) \(a_{12}=+0.000000000\) \(a_{13}=+0.393804665\) \(a_{14}=+0.000000000\) \(a_{15}=+0.993303197\)
\(a_{16}=+0.000000000\) \(a_{17}=-0.326046380\) \(a_{18}=+0.000000000\) \(a_{19}=+1.134369164\) \(a_{20}=+0.000000000\)
\(a_{21}=-0.800604692\) \(a_{22}=+0.000000000\) \(a_{23}=-0.583605173\) \(a_{24}=+0.000000000\) \(a_{25}=-0.720739480\)
\(a_{26}=+0.000000000\) \(a_{27}=+2.881664296\) \(a_{28}=+0.000000000\) \(a_{29}=-0.334407520\) \(a_{30}=+0.000000000\)
\(a_{31}=-1.734771800\) \(a_{32}=+0.000000000\) \(a_{33}=+0.312636863\) \(a_{34}=+0.000000000\) \(a_{35}=-0.225084630\)
\(a_{36}=+0.000000000\) \(a_{37}=+0.151106500\) \(a_{38}=+0.000000000\) \(a_{39}=+0.740215064\) \(a_{40}=+0.000000000\)
\(a_{41}=-1.279933000\) \(a_{42}=+0.000000000\) \(a_{43}=+1.187390000\) \(a_{44}=+0.000000000\) \(a_{45}=+1.338611612\)
\(a_{46}=+0.000000000\) \(a_{47}=-0.940999985\) \(a_{48}=+0.000000000\) \(a_{49}=-0.818581264\) \(a_{50}=+0.000000000\)
\(a_{51}=-0.612853182\) \(a_{52}=+0.000000000\) \(a_{53}=-0.879997253\) \(a_{54}=+0.000000000\) \(a_{55}=+0.087895754\)
\(a_{56}=+0.000000000\) \(a_{57}=+2.132217359\) \(a_{58}=+0.000000000\) \(a_{59}=+1.099609375\) \(a_{60}=+0.000000000\)
\(a_{61}=+0.000000000\) \(a_{62}=+0.000000000\) \(a_{63}=-1.078924079\) \(a_{64}=+0.000000000\) \(a_{65}=+0.208106492\)
\(a_{66}=+0.000000000\)

Showing all 66 available coefficients

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