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: \( 26.7558383271 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=-0.230925038\) \(a_{4}=+0.000000000\) \(a_{5}=+1.186474211\)
\(a_{6}=+0.000000000\) \(a_{7}=+1.738114407\) \(a_{8}=+0.000000000\) \(a_{9}=-0.946673627\) \(a_{10}=+0.000000000\)
\(a_{11}=-0.742275570\) \(a_{12}=+0.000000000\) \(a_{13}=-1.583602814\) \(a_{14}=+0.000000000\) \(a_{15}=-0.273986602\)
\(a_{16}=+0.000000000\) \(a_{17}=-1.080589295\) \(a_{18}=+0.000000000\) \(a_{19}=+0.916797176\) \(a_{20}=+0.000000000\)
\(a_{21}=-0.401374135\) \(a_{22}=+0.000000000\) \(a_{23}=+0.215362363\) \(a_{24}=+0.000000000\) \(a_{25}=+0.407721054\)
\(a_{26}=+0.000000000\) \(a_{27}=+0.449535680\) \(a_{28}=+0.000000000\) \(a_{29}=-0.402704461\) \(a_{30}=+0.000000000\)
\(a_{31}=-0.792828755\) \(a_{32}=+0.000000000\) \(a_{33}=+0.171410009\) \(a_{34}=+0.000000000\) \(a_{35}=+2.062227696\)
\(a_{36}=+0.000000000\) \(a_{37}=-1.280776806\) \(a_{38}=+0.000000000\) \(a_{39}=+0.365697305\) \(a_{40}=+0.000000000\)
\(a_{41}=-1.418610000\) \(a_{42}=+0.000000000\) \(a_{43}=+0.583673604\) \(a_{44}=+0.000000000\) \(a_{45}=-1.120120280\)
\(a_{46}=+0.000000000\)

Showing all 46 available coefficients

Rows: Cols: