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: \( 22.6755943543 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=-0.004663343\) \(a_{4}=+0.000000000\) \(a_{5}=-1.446412486\)
\(a_{6}=+0.000000000\) \(a_{7}=+1.764569093\) \(a_{8}=+0.000000000\) \(a_{9}=-0.999978253\) \(a_{10}=+0.000000000\)
\(a_{11}=-1.072272133\) \(a_{12}=+0.000000000\) \(a_{13}=+0.084007873\) \(a_{14}=+0.000000000\) \(a_{15}=+0.006745118\)
\(a_{16}=+0.000000000\) \(a_{17}=-0.612878109\) \(a_{18}=+0.000000000\) \(a_{19}=+0.951345129\) \(a_{20}=+0.000000000\)
\(a_{21}=-0.008228792\) \(a_{22}=+0.000000000\) \(a_{23}=-1.518744545\) \(a_{24}=+0.000000000\) \(a_{25}=+1.092109056\)
\(a_{26}=+0.000000000\) \(a_{27}=+0.009326388\) \(a_{28}=+0.000000000\) \(a_{29}=+0.884325080\) \(a_{30}=+0.000000000\)
\(a_{31}=-0.356137839\) \(a_{32}=+0.000000000\) \(a_{33}=+0.004912554\) \(a_{34}=+0.000000000\) \(a_{35}=-2.552916799\)
\(a_{36}=+0.000000000\) \(a_{37}=+0.635181003\) \(a_{38}=+0.000000000\) \(a_{39}=-0.025583129\) \(a_{40}=+0.000000000\)
\(a_{41}=+0.906341331\) \(a_{42}=+0.000000000\)

Showing all 42 available coefficients

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