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: \( 15.7434456453 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=+0.976765835\) \(a_{4}=+0.000000000\) \(a_{5}=+0.336980889\)
\(a_{6}=+0.000000000\) \(a_{7}=-1.371800902\) \(a_{8}=+0.000000000\) \(a_{9}=-0.045928503\) \(a_{10}=+0.000000000\)
\(a_{11}=-1.256721790\) \(a_{12}=+0.000000000\) \(a_{13}=+0.799267079\) \(a_{14}=+0.000000000\) \(a_{15}=+0.329151420\)
\(a_{16}=+0.000000000\) \(a_{17}=+0.959524830\) \(a_{18}=+0.000000000\) \(a_{19}=-1.680167300\) \(a_{20}=+0.000000000\)
\(a_{21}=-1.339928254\) \(a_{22}=+0.000000000\) \(a_{23}=-0.834699988\) \(a_{24}=+0.000000000\) \(a_{25}=-0.886443880\)
\(a_{26}=+0.000000000\) \(a_{27}=-1.021627228\) \(a_{28}=+0.000000000\) \(a_{29}=-0.885999680\) \(a_{30}=+0.000000000\)
\(a_{31}=+1.563000000\) \(a_{32}=+0.000000000\) \(a_{33}=-1.227522908\) \(a_{34}=+0.000000000\) \(a_{35}=-0.462270687\)
\(a_{36}=+0.000000000\) \(a_{37}=+0.000000000\) \(a_{38}=+0.000000000\) \(a_{39}=+0.780696776\) \(a_{40}=+0.000000000\)

Showing all 40 available coefficients

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