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: \( 21.0692394685 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=-0.780963982\) \(a_{4}=+0.000000000\) \(a_{5}=+0.315390584\)
\(a_{6}=+0.000000000\) \(a_{7}=-0.014510176\) \(a_{8}=+0.000000000\) \(a_{9}=-0.390095259\) \(a_{10}=+0.000000000\)
\(a_{11}=-0.530213717\) \(a_{12}=+0.000000000\) \(a_{13}=+1.750808446\) \(a_{14}=+0.000000000\) \(a_{15}=-0.246308686\)
\(a_{16}=+0.000000000\) \(a_{17}=+0.558522890\) \(a_{18}=+0.000000000\) \(a_{19}=+0.555277773\) \(a_{20}=+0.000000000\)
\(a_{21}=+0.011331924\) \(a_{22}=+0.000000000\) \(a_{23}=-0.712755493\) \(a_{24}=+0.000000000\) \(a_{25}=-0.900528888\)
\(a_{26}=+0.000000000\) \(a_{27}=+1.085613436\) \(a_{28}=+0.000000000\) \(a_{29}=+1.516687293\) \(a_{30}=+0.000000000\)
\(a_{31}=-0.565024579\) \(a_{32}=+0.000000000\) \(a_{33}=+0.413865856\) \(a_{34}=+0.000000000\) \(a_{35}=-0.005349933\)
\(a_{36}=+0.000000000\) \(a_{37}=-1.767810973\) \(a_{38}=+0.000000000\) \(a_{39}=-1.343487056\) \(a_{40}=+0.000000000\)

Showing all 40 available coefficients

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