Properties

Level $4$
Weight $0$
Character 4.1
Symmetry even
Fricke sign $-1$

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Maass form invariants

Level: \( 4 = 2^{2} \)
Weight: \( 0 \)
Character: 4.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 16.0935923774 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=-1.811289379\) \(a_{4}=+0.000000000\) \(a_{5}=-0.503963586\)
\(a_{6}=+0.000000000\) \(a_{7}=+1.473795289\) \(a_{8}=+0.000000000\) \(a_{9}=+2.280769215\) \(a_{10}=+0.000000000\)
\(a_{11}=-0.562217518\) \(a_{12}=+0.000000000\) \(a_{13}=+0.012097481\) \(a_{14}=+0.000000000\) \(a_{15}=+0.912823891\)
\(a_{16}=+0.000000000\) \(a_{17}=+0.409607001\) \(a_{18}=+0.000000000\) \(a_{19}=+0.221660003\) \(a_{20}=+0.000000000\)
\(a_{21}=-2.669469753\) \(a_{22}=+0.000000000\) \(a_{23}=-0.244399995\) \(a_{24}=+0.000000000\) \(a_{25}=-0.746020704\)
\(a_{26}=+0.000000000\) \(a_{27}=-2.319843676\) \(a_{28}=+0.000000000\) \(a_{29}=+0.969970703\) \(a_{30}=+0.000000000\)
\(a_{31}=-1.320007324\) \(a_{32}=+0.000000000\) \(a_{33}=+1.018338619\) \(a_{34}=+0.000000000\) \(a_{35}=-0.742739159\)
\(a_{36}=+0.000000000\) \(a_{37}=+0.000000000\) \(a_{38}=+0.000000000\) \(a_{39}=-0.021912039\) \(a_{40}=+0.000000000\)

Showing all 40 available coefficients

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