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: \( 24.843282219 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=+0.504352691\) \(a_{4}=+0.000000000\) \(a_{5}=-1.437694437\)
\(a_{6}=+0.000000000\) \(a_{7}=-1.384944551\) \(a_{8}=+0.000000000\) \(a_{9}=-0.745628363\) \(a_{10}=+0.000000000\)
\(a_{11}=-1.615167638\) \(a_{12}=+0.000000000\) \(a_{13}=-0.817669665\) \(a_{14}=+0.000000000\) \(a_{15}=-0.725105058\)
\(a_{16}=+0.000000000\) \(a_{17}=+0.424965040\) \(a_{18}=+0.000000000\) \(a_{19}=+1.124122207\) \(a_{20}=+0.000000000\)
\(a_{21}=-0.698500511\) \(a_{22}=+0.000000000\) \(a_{23}=+0.624902986\) \(a_{24}=+0.000000000\) \(a_{25}=+1.066965295\)
\(a_{26}=+0.000000000\) \(a_{27}=-0.880412365\) \(a_{28}=+0.000000000\) \(a_{29}=-0.624088996\) \(a_{30}=+0.000000000\)
\(a_{31}=+0.634026415\) \(a_{32}=+0.000000000\) \(a_{33}=-0.814613740\) \(a_{34}=+0.000000000\) \(a_{35}=+1.991129969\)
\(a_{36}=+0.000000000\) \(a_{37}=+0.039668121\) \(a_{38}=+0.000000000\) \(a_{39}=-0.411788499\) \(a_{40}=+0.000000000\)
\(a_{41}=-1.145674288\) \(a_{42}=+0.000000000\) \(a_{43}=-1.332141075\) \(a_{44}=+0.000000000\) \(a_{45}=+1.226540215\)
\(a_{46}=+0.000000000\)

Showing all 46 available coefficients

Rows: Cols: