Properties

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

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Maass form invariants

Level: \( 4 = 2^{2} \)
Weight: \( 0 \)
Character: 4.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 20.063994817 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=-1.460162404\) \(a_{4}=+0.000000000\) \(a_{5}=+0.082418048\)
\(a_{6}=+0.000000000\) \(a_{7}=-0.360194317\) \(a_{8}=+0.000000000\) \(a_{9}=+1.132074246\) \(a_{10}=+0.000000000\)
\(a_{11}=-1.702648133\) \(a_{12}=+0.000000000\) \(a_{13}=-1.367994006\) \(a_{14}=+0.000000000\) \(a_{15}=-0.120343736\)
\(a_{16}=+0.000000000\) \(a_{17}=-1.620738399\) \(a_{18}=+0.000000000\) \(a_{19}=+1.081702008\) \(a_{20}=+0.000000000\)
\(a_{21}=+0.525942200\) \(a_{22}=+0.000000000\) \(a_{23}=-0.196732036\) \(a_{24}=+0.000000000\) \(a_{25}=-0.993207256\)
\(a_{26}=+0.000000000\) \(a_{27}=-0.192849869\) \(a_{28}=+0.000000000\) \(a_{29}=-1.150522580\) \(a_{30}=+0.000000000\)
\(a_{31}=+0.620131364\) \(a_{32}=+0.000000000\) \(a_{33}=+2.486148249\) \(a_{34}=+0.000000000\) \(a_{35}=-0.029411343\)
\(a_{36}=+0.000000000\) \(a_{37}=+0.841693408\) \(a_{38}=+0.000000000\) \(a_{39}=+1.992451895\) \(a_{40}=+0.000000000\)

Showing all 40 available coefficients

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