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: \( 22.5317665089 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=-1.813932993\) \(a_{4}=+0.000000000\) \(a_{5}=-1.519601945\)
\(a_{6}=+0.000000000\) \(a_{7}=-0.642568210\) \(a_{8}=+0.000000000\) \(a_{9}=+2.290352902\) \(a_{10}=+0.000000000\)
\(a_{11}=-0.093347025\) \(a_{12}=+0.000000000\) \(a_{13}=-0.060279605\) \(a_{14}=+0.000000000\) \(a_{15}=+2.756456103\)
\(a_{16}=+0.000000000\) \(a_{17}=+1.571508931\) \(a_{18}=+0.000000000\) \(a_{19}=-0.249337970\) \(a_{20}=+0.000000000\)
\(a_{21}=+1.165575677\) \(a_{22}=+0.000000000\) \(a_{23}=-0.260327141\) \(a_{24}=+0.000000000\) \(a_{25}=+1.309190072\)
\(a_{26}=+0.000000000\) \(a_{27}=-2.340613694\) \(a_{28}=+0.000000000\) \(a_{29}=+0.025112835\) \(a_{30}=+0.000000000\)
\(a_{31}=+1.072182410\) \(a_{32}=+0.000000000\) \(a_{33}=+0.169337854\) \(a_{34}=+0.000000000\) \(a_{35}=+0.976630069\)
\(a_{36}=+0.000000000\) \(a_{37}=+0.340687273\) \(a_{38}=+0.000000000\) \(a_{39}=+0.129755229\) \(a_{40}=+0.000000000\)

Showing all 40 available coefficients

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