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: \( 26.4600305542 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=+1.478838560\) \(a_{4}=+0.000000000\) \(a_{5}=+0.266563541\)
\(a_{6}=+0.000000000\) \(a_{7}=-1.901932779\) \(a_{8}=+0.000000000\) \(a_{9}=+1.186963487\) \(a_{10}=+0.000000000\)
\(a_{11}=+1.378526875\) \(a_{12}=+0.000000000\) \(a_{13}=-1.056658024\) \(a_{14}=+0.000000000\) \(a_{15}=+0.394204444\)
\(a_{16}=+0.000000000\) \(a_{17}=+0.635662049\) \(a_{18}=+0.000000000\) \(a_{19}=-0.072180290\) \(a_{20}=+0.000000000\)
\(a_{21}=-2.812651533\) \(a_{22}=+0.000000000\) \(a_{23}=-0.558731179\) \(a_{24}=+0.000000000\) \(a_{25}=-0.928943878\)
\(a_{26}=+0.000000000\) \(a_{27}=+0.276488814\) \(a_{28}=+0.000000000\) \(a_{29}=-1.081966243\) \(a_{30}=+0.000000000\)
\(a_{31}=-0.836623479\) \(a_{32}=+0.000000000\) \(a_{33}=+2.038618660\) \(a_{34}=+0.000000000\) \(a_{35}=-0.506986159\)
\(a_{36}=+0.000000000\) \(a_{37}=+0.531472302\) \(a_{38}=+0.000000000\) \(a_{39}=-1.562674968\) \(a_{40}=+0.000000000\)
\(a_{41}=+0.082295360\) \(a_{42}=+0.000000000\) \(a_{43}=-0.445681921\) \(a_{44}=+0.000000000\) \(a_{45}=+0.280846575\)
\(a_{46}=+0.000000000\) \(a_{47}=-0.588568612\)

Showing all 47 available coefficients

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