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: \( 24.7506671044 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=+1.252636588\) \(a_{4}=+0.000000000\) \(a_{5}=+0.935169188\)
\(a_{6}=+0.000000000\) \(a_{7}=-0.184225463\) \(a_{8}=+0.000000000\) \(a_{9}=+0.569098422\) \(a_{10}=+0.000000000\)
\(a_{11}=-1.353295203\) \(a_{12}=+0.000000000\) \(a_{13}=-0.500788475\) \(a_{14}=+0.000000000\) \(a_{15}=+1.171427141\)
\(a_{16}=+0.000000000\) \(a_{17}=-1.792198947\) \(a_{18}=+0.000000000\) \(a_{19}=-1.283496349\) \(a_{20}=+0.000000000\)
\(a_{21}=-0.230767556\) \(a_{22}=+0.000000000\) \(a_{23}=-1.107373582\) \(a_{24}=+0.000000000\) \(a_{25}=-0.125458590\)
\(a_{26}=+0.000000000\) \(a_{27}=-0.539763082\) \(a_{28}=+0.000000000\) \(a_{29}=+1.532659329\) \(a_{30}=+0.000000000\)
\(a_{31}=+0.111171884\) \(a_{32}=+0.000000000\) \(a_{33}=-1.695187120\) \(a_{34}=+0.000000000\) \(a_{35}=-0.172282805\)
\(a_{36}=+0.000000000\) \(a_{37}=+0.457523567\) \(a_{38}=+0.000000000\) \(a_{39}=-0.627464294\) \(a_{40}=+0.000000000\)
\(a_{41}=+1.442991423\) \(a_{42}=+0.000000000\) \(a_{43}=+0.773519388\) \(a_{44}=+0.000000000\) \(a_{45}=+0.450729757\)
\(a_{46}=+0.000000000\)

Showing all 46 available coefficients

Rows: Cols: