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: \( 23.3156378318 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=-0.358693311\) \(a_{4}=+0.000000000\) \(a_{5}=+1.269337234\)
\(a_{6}=+0.000000000\) \(a_{7}=+0.430923344\) \(a_{8}=+0.000000000\) \(a_{9}=-0.871339109\) \(a_{10}=+0.000000000\)
\(a_{11}=-1.363839010\) \(a_{12}=+0.000000000\) \(a_{13}=+0.007230479\) \(a_{14}=+0.000000000\) \(a_{15}=-0.455302775\)
\(a_{16}=+0.000000000\) \(a_{17}=+1.337332862\) \(a_{18}=+0.000000000\) \(a_{19}=-0.313762362\) \(a_{20}=+0.000000000\)
\(a_{21}=-0.154569321\) \(a_{22}=+0.000000000\) \(a_{23}=+0.138787284\) \(a_{24}=+0.000000000\) \(a_{25}=+0.611217014\)
\(a_{26}=+0.000000000\) \(a_{27}=+0.671236824\) \(a_{28}=+0.000000000\) \(a_{29}=-1.923803921\) \(a_{30}=+0.000000000\)
\(a_{31}=-0.126166600\) \(a_{32}=+0.000000000\) \(a_{33}=+0.489195807\) \(a_{34}=+0.000000000\) \(a_{35}=+0.546972490\)
\(a_{36}=+0.000000000\) \(a_{37}=+0.870589843\) \(a_{38}=+0.000000000\) \(a_{39}=-0.002789195\) \(a_{40}=+0.000000000\)
\(a_{41}=+1.635105503\) \(a_{42}=+0.000000000\) \(a_{43}=-1.500496991\) \(a_{44}=+0.000000000\)

Showing all 44 available coefficients

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