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: \( 24.354473593 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=-0.845723608\) \(a_{4}=+0.000000000\) \(a_{5}=-0.580896257\)
\(a_{6}=+0.000000000\) \(a_{7}=+0.037948806\) \(a_{8}=+0.000000000\) \(a_{9}=-0.284751578\) \(a_{10}=+0.000000000\)
\(a_{11}=+1.210549242\) \(a_{12}=+0.000000000\) \(a_{13}=-0.592908139\) \(a_{14}=+0.000000000\) \(a_{15}=+0.491277678\)
\(a_{16}=+0.000000000\) \(a_{17}=+0.039067659\) \(a_{18}=+0.000000000\) \(a_{19}=+1.884089151\) \(a_{20}=+0.000000000\)
\(a_{21}=-0.032094201\) \(a_{22}=+0.000000000\) \(a_{23}=+0.229935140\) \(a_{24}=+0.000000000\) \(a_{25}=-0.662559539\)
\(a_{26}=+0.000000000\) \(a_{27}=+1.086544740\) \(a_{28}=+0.000000000\) \(a_{29}=+0.698221691\) \(a_{30}=+0.000000000\)
\(a_{31}=-0.901906230\) \(a_{32}=+0.000000000\) \(a_{33}=-1.023789917\) \(a_{34}=+0.000000000\) \(a_{35}=-0.022045257\)
\(a_{36}=+0.000000000\) \(a_{37}=+0.524013392\) \(a_{38}=+0.000000000\) \(a_{39}=+0.501538963\) \(a_{40}=+0.000000000\)
\(a_{41}=+0.259680736\) \(a_{42}=+0.000000000\) \(a_{43}=+1.761651043\) \(a_{44}=+0.000000000\) \(a_{45}=+0.211894792\)

Showing all 45 available coefficients

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