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: \( 25.6508724359 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=+0.177698852\) \(a_{4}=+0.000000000\) \(a_{5}=-0.868909136\)
\(a_{6}=+0.000000000\) \(a_{7}=+0.788224141\) \(a_{8}=+0.000000000\) \(a_{9}=-0.968423118\) \(a_{10}=+0.000000000\)
\(a_{11}=+0.305329576\) \(a_{12}=+0.000000000\) \(a_{13}=+1.027179150\) \(a_{14}=+0.000000000\) \(a_{15}=-0.154404156\)
\(a_{16}=+0.000000000\) \(a_{17}=+0.831763595\) \(a_{18}=+0.000000000\) \(a_{19}=-1.017726952\) \(a_{20}=+0.000000000\)
\(a_{21}=+0.140066525\) \(a_{22}=+0.000000000\) \(a_{23}=+0.262914722\) \(a_{24}=+0.000000000\) \(a_{25}=-0.244996913\)
\(a_{26}=+0.000000000\) \(a_{27}=-0.349786528\) \(a_{28}=+0.000000000\) \(a_{29}=-0.765470489\) \(a_{30}=+0.000000000\)
\(a_{31}=+1.784307740\) \(a_{32}=+0.000000000\) \(a_{33}=+0.054256734\) \(a_{34}=+0.000000000\) \(a_{35}=-0.684894991\)
\(a_{36}=+0.000000000\) \(a_{37}=-0.983279828\) \(a_{38}=+0.000000000\) \(a_{39}=+0.182523108\) \(a_{40}=+0.000000000\)
\(a_{41}=-0.279300719\) \(a_{42}=+0.000000000\) \(a_{43}=+0.277546237\) \(a_{44}=+0.000000000\) \(a_{45}=+0.843752028\)
\(a_{46}=+0.000000000\)

Showing all 46 available coefficients

Rows: Cols: