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: \( 9.19652685256 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=+0.950131492\) \(a_{4}=+0.000000000\) \(a_{5}=+1.966231599\)
\(a_{6}=+0.000000000\) \(a_{7}=-0.621438342\) \(a_{8}=+0.000000000\) \(a_{9}=-0.097250148\) \(a_{10}=+0.000000000\)
\(a_{11}=+0.637019940\) \(a_{12}=+0.000000000\) \(a_{13}=+0.526602786\) \(a_{14}=+0.000000000\) \(a_{15}=+1.868178562\)
\(a_{16}=+0.000000000\) \(a_{17}=+0.583561675\) \(a_{18}=+0.000000000\) \(a_{19}=+0.780057295\) \(a_{20}=+0.000000000\)
\(a_{21}=-0.590448139\) \(a_{22}=+0.000000000\) \(a_{23}=-0.532962801\) \(a_{24}=+0.000000000\) \(a_{25}=+2.866066700\)
\(a_{26}=+0.000000000\) \(a_{27}=-1.042531920\) \(a_{28}=+0.000000000\) \(a_{29}=-0.778765175\) \(a_{30}=+0.000000000\)
\(a_{31}=+0.022887457\) \(a_{32}=+0.000000000\) \(a_{33}=+0.605252706\) \(a_{34}=+0.000000000\) \(a_{35}=-1.221891705\)
\(a_{36}=+0.000000000\) \(a_{37}=+1.103987510\) \(a_{38}=+0.000000000\) \(a_{39}=+0.500341891\) \(a_{40}=+0.000000000\)
\(a_{41}=+0.498661300\) \(a_{42}=+0.000000000\) \(a_{43}=-1.007197000\) \(a_{44}=+0.000000000\) \(a_{45}=-0.191216314\)
\(a_{46}=+0.000000000\) \(a_{47}=-0.393130001\) \(a_{48}=+0.000000000\) \(a_{49}=-0.613814387\) \(a_{50}=+0.000000000\)
\(a_{51}=+0.554460325\) \(a_{52}=+0.000000000\) \(a_{53}=+0.398600101\) \(a_{54}=+0.000000000\) \(a_{55}=+1.252528735\)
\(a_{56}=+0.000000000\) \(a_{57}=+0.741157002\) \(a_{58}=+0.000000000\) \(a_{59}=-1.589996338\) \(a_{60}=+0.000000000\)
\(a_{61}=-1.070007324\) \(a_{62}=+0.000000000\) \(a_{63}=+0.060434971\) \(a_{64}=+0.000000000\) \(a_{65}=+1.035423039\)
\(a_{66}=+0.000000000\)

Showing all 66 available coefficients

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