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: \( 25.304242743 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=+0.157681768\) \(a_{4}=+0.000000000\) \(a_{5}=+1.617605932\)
\(a_{6}=+0.000000000\) \(a_{7}=-0.095101013\) \(a_{8}=+0.000000000\) \(a_{9}=-0.975136460\) \(a_{10}=+0.000000000\)
\(a_{11}=+1.469195272\) \(a_{12}=+0.000000000\) \(a_{13}=+1.359706977\) \(a_{14}=+0.000000000\) \(a_{15}=+0.255066963\)
\(a_{16}=+0.000000000\) \(a_{17}=-0.224124880\) \(a_{18}=+0.000000000\) \(a_{19}=+0.775911958\) \(a_{20}=+0.000000000\)
\(a_{21}=-0.014995696\) \(a_{22}=+0.000000000\) \(a_{23}=-0.969836496\) \(a_{24}=+0.000000000\) \(a_{25}=+1.616648950\)
\(a_{26}=+0.000000000\) \(a_{27}=-0.311443009\) \(a_{28}=+0.000000000\) \(a_{29}=-0.491822070\) \(a_{30}=+0.000000000\)
\(a_{31}=-0.453674388\) \(a_{32}=+0.000000000\) \(a_{33}=+0.231665615\) \(a_{34}=+0.000000000\) \(a_{35}=-0.153834884\)
\(a_{36}=+0.000000000\) \(a_{37}=+1.755474754\) \(a_{38}=+0.000000000\) \(a_{39}=+0.214041620\) \(a_{40}=+0.000000000\)
\(a_{41}=-1.380580079\) \(a_{42}=+0.000000000\) \(a_{43}=-0.311141755\) \(a_{44}=+0.000000000\) \(a_{45}=-1.824478205\)
\(a_{46}=+0.000000000\)

Showing all 46 available coefficients

Rows: Cols: