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: \( 22.1020557995 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=+0.635882391\) \(a_{4}=+0.000000000\) \(a_{5}=+0.247564814\)
\(a_{6}=+0.000000000\) \(a_{7}=+0.123712912\) \(a_{8}=+0.000000000\) \(a_{9}=-0.595653584\) \(a_{10}=+0.000000000\)
\(a_{11}=+0.660474148\) \(a_{12}=+0.000000000\) \(a_{13}=-0.986096571\) \(a_{14}=+0.000000000\) \(a_{15}=+0.157422106\)
\(a_{16}=+0.000000000\) \(a_{17}=-1.389517415\) \(a_{18}=+0.000000000\) \(a_{19}=+0.161067733\) \(a_{20}=+0.000000000\)
\(a_{21}=+0.078666862\) \(a_{22}=+0.000000000\) \(a_{23}=+0.777817694\) \(a_{24}=+0.000000000\) \(a_{25}=-0.938711663\)
\(a_{26}=+0.000000000\) \(a_{27}=-1.014648016\) \(a_{28}=+0.000000000\) \(a_{29}=+0.337045678\) \(a_{30}=+0.000000000\)
\(a_{31}=+1.319073954\) \(a_{32}=+0.000000000\) \(a_{33}=+0.419983355\) \(a_{34}=+0.000000000\) \(a_{35}=+0.030622607\)
\(a_{36}=+0.000000000\) \(a_{37}=+0.729083651\) \(a_{38}=+0.000000000\) \(a_{39}=-0.627103544\) \(a_{40}=+0.000000000\)
\(a_{41}=-1.880875015\) \(a_{42}=+0.000000000\) \(a_{43}=-1.486829690\)

Showing all 43 available coefficients

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