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: \( 19.7785769776 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=+0.381662138\) \(a_{4}=+0.000000000\) \(a_{5}=+1.846681996\)
\(a_{6}=+0.000000000\) \(a_{7}=-1.416290749\) \(a_{8}=+0.000000000\) \(a_{9}=-0.854334012\) \(a_{10}=+0.000000000\)
\(a_{11}=+0.082682759\) \(a_{12}=+0.000000000\) \(a_{13}=-1.260163171\) \(a_{14}=+0.000000000\) \(a_{15}=+0.704808599\)
\(a_{16}=+0.000000000\) \(a_{17}=+0.010560711\) \(a_{18}=+0.000000000\) \(a_{19}=-0.501042639\) \(a_{20}=+0.000000000\)
\(a_{21}=-0.540544555\) \(a_{22}=+0.000000000\) \(a_{23}=-0.165586251\) \(a_{24}=+0.000000000\) \(a_{25}=+2.410234395\)
\(a_{26}=+0.000000000\) \(a_{27}=-0.707729078\) \(a_{28}=+0.000000000\) \(a_{29}=+0.391523392\) \(a_{30}=+0.000000000\)
\(a_{31}=-1.331913302\) \(a_{32}=+0.000000000\) \(a_{33}=+0.031560956\) \(a_{34}=+0.000000000\) \(a_{35}=-2.615385264\)
\(a_{36}=+0.000000000\) \(a_{37}=-0.936629959\) \(a_{38}=+0.000000000\) \(a_{39}=-0.477067688\) \(a_{40}=+0.000000000\)
\(a_{41}=-0.478754151\)

Showing all 41 available coefficients

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