Properties

Level $4$
Weight $0$
Character 4.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 4 = 2^{2} \)
Weight: \( 0 \)
Character: 4.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 21.2608445041 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=-0.006778395\) \(a_{4}=+0.000000000\) \(a_{5}=-0.877596096\)
\(a_{6}=+0.000000000\) \(a_{7}=-0.839043314\) \(a_{8}=+0.000000000\) \(a_{9}=-0.999954053\) \(a_{10}=+0.000000000\)
\(a_{11}=+0.119571236\) \(a_{12}=+0.000000000\) \(a_{13}=-0.335692246\) \(a_{14}=+0.000000000\) \(a_{15}=+0.005948693\)
\(a_{16}=+0.000000000\) \(a_{17}=+0.807906947\) \(a_{18}=+0.000000000\) \(a_{19}=-1.271840800\) \(a_{20}=+0.000000000\)
\(a_{21}=+0.005687366\) \(a_{22}=+0.000000000\) \(a_{23}=+1.307581371\) \(a_{24}=+0.000000000\) \(a_{25}=-0.229825138\)
\(a_{26}=+0.000000000\) \(a_{27}=+0.013556228\) \(a_{28}=+0.000000000\) \(a_{29}=-0.573735188\) \(a_{30}=+0.000000000\)
\(a_{31}=-1.555194356\) \(a_{32}=+0.000000000\) \(a_{33}=-0.000983250\) \(a_{34}=+0.000000000\) \(a_{35}=+0.734517663\)
\(a_{36}=+0.000000000\) \(a_{37}=+1.598712504\) \(a_{38}=+0.000000000\) \(a_{39}=-0.109328037\) \(a_{40}=+0.000000000\)

Showing all 40 available coefficients

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