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: \( 19.6990197959 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=-0.950226641\) \(a_{4}=+0.000000000\) \(a_{5}=-1.373095276\)
\(a_{6}=+0.000000000\) \(a_{7}=+1.217107141\) \(a_{8}=+0.000000000\) \(a_{9}=-0.097069331\) \(a_{10}=+0.000000000\)
\(a_{11}=+1.666652215\) \(a_{12}=+0.000000000\) \(a_{13}=-0.077206275\) \(a_{14}=+0.000000000\) \(a_{15}=+1.304751711\)
\(a_{16}=+0.000000000\) \(a_{17}=-0.194925255\) \(a_{18}=+0.000000000\) \(a_{19}=-0.116078318\) \(a_{20}=+0.000000000\)
\(a_{21}=-1.156527633\) \(a_{22}=+0.000000000\) \(a_{23}=+1.061118309\) \(a_{24}=+0.000000000\) \(a_{25}=+0.885390262\)
\(a_{26}=+0.000000000\) \(a_{27}=+1.042460614\) \(a_{28}=+0.000000000\) \(a_{29}=-1.772211863\) \(a_{30}=+0.000000000\)
\(a_{31}=+0.637445376\) \(a_{32}=+0.000000000\) \(a_{33}=-1.582092863\) \(a_{34}=+0.000000000\) \(a_{35}=-1.650055350\)
\(a_{36}=+0.000000000\)

Showing all 36 available coefficients

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