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: \( 17.195127212 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=+0.320386779\) \(a_{4}=+0.000000000\) \(a_{5}=-0.023557235\)
\(a_{6}=+0.000000000\) \(a_{7}=+0.193414423\) \(a_{8}=+0.000000000\) \(a_{9}=-0.897352312\) \(a_{10}=+0.000000000\)
\(a_{11}=+0.776025173\) \(a_{12}=+0.000000000\) \(a_{13}=-1.015760804\) \(a_{14}=+0.000000000\) \(a_{15}=-0.007547427\)
\(a_{16}=+0.000000000\) \(a_{17}=+0.291588179\) \(a_{18}=+0.000000000\) \(a_{19}=+1.290915907\) \(a_{20}=+0.000000000\)
\(a_{21}=+0.061967424\) \(a_{22}=+0.000000000\) \(a_{23}=-1.598129800\) \(a_{24}=+0.000000000\) \(a_{25}=-0.999445057\)
\(a_{26}=+0.000000000\) \(a_{27}=-0.607886596\) \(a_{28}=+0.000000000\) \(a_{29}=-1.780451000\) \(a_{30}=+0.000000000\)
\(a_{31}=-1.022230000\) \(a_{32}=+0.000000000\) \(a_{33}=+0.248628206\) \(a_{34}=+0.000000000\) \(a_{35}=-0.004556309\)
\(a_{36}=+0.000000000\)

Showing all 36 available coefficients

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