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: \( 24.3902808035 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=-1.519920284\) \(a_{4}=+0.000000000\) \(a_{5}=-0.002695784\)
\(a_{6}=+0.000000000\) \(a_{7}=+1.296679086\) \(a_{8}=+0.000000000\) \(a_{9}=+1.310157670\) \(a_{10}=+0.000000000\)
\(a_{11}=-0.785644093\) \(a_{12}=+0.000000000\) \(a_{13}=+1.129602659\) \(a_{14}=+0.000000000\) \(a_{15}=+0.004097377\)
\(a_{16}=+0.000000000\) \(a_{17}=-1.379605356\) \(a_{18}=+0.000000000\) \(a_{19}=-1.501914930\) \(a_{20}=+0.000000000\)
\(a_{21}=-1.970848845\) \(a_{22}=+0.000000000\) \(a_{23}=+1.503589931\) \(a_{24}=+0.000000000\) \(a_{25}=-0.999992739\)
\(a_{26}=+0.000000000\) \(a_{27}=-0.471414950\) \(a_{28}=+0.000000000\) \(a_{29}=-0.168339150\) \(a_{30}=+0.000000000\)
\(a_{31}=-0.006879685\) \(a_{32}=+0.000000000\) \(a_{33}=+1.194125350\) \(a_{34}=+0.000000000\) \(a_{35}=-0.003434311\)
\(a_{36}=+0.000000000\) \(a_{37}=+0.733655020\) \(a_{38}=+0.000000000\) \(a_{39}=-1.714939532\) \(a_{40}=+0.000000000\)
\(a_{41}=-1.520873603\) \(a_{42}=+0.000000000\) \(a_{43}=+0.809714667\) \(a_{44}=+0.000000000\) \(a_{45}=+0.247623712\)

Showing all 45 available coefficients

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