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: \( 18.6207750965 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=+0.935740064\) \(a_{4}=+0.000000000\) \(a_{5}=-0.378195042\)
\(a_{6}=+0.000000000\) \(a_{7}=+0.609246124\) \(a_{8}=+0.000000000\) \(a_{9}=-0.124390533\) \(a_{10}=+0.000000000\)
\(a_{11}=-1.842462032\) \(a_{12}=+0.000000000\) \(a_{13}=+0.510161953\) \(a_{14}=+0.000000000\) \(a_{15}=-0.353892252\)
\(a_{16}=+0.000000000\) \(a_{17}=-0.670402073\) \(a_{18}=+0.000000000\) \(a_{19}=-0.092326876\) \(a_{20}=+0.000000000\)
\(a_{21}=+0.570096007\) \(a_{22}=+0.000000000\) \(a_{23}=+1.753646280\) \(a_{24}=+0.000000000\) \(a_{25}=-0.856968521\)
\(a_{26}=+0.000000000\) \(a_{27}=-1.052137368\) \(a_{28}=+0.000000000\) \(a_{29}=-0.184138554\) \(a_{30}=+0.000000000\)
\(a_{31}=-1.744317084\) \(a_{32}=+0.000000000\) \(a_{33}=-1.724070992\) \(a_{34}=+0.000000000\) \(a_{35}=-0.230757712\)
\(a_{36}=+0.000000000\) \(a_{37}=-0.921264176\) \(a_{38}=+0.000000000\) \(a_{39}=+0.549568845\) \(a_{40}=+0.000000000\)

Showing all 40 available coefficients

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