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: \( 25.5947866217 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=-1.674829466\) \(a_{4}=+0.000000000\) \(a_{5}=+1.402350333\)
\(a_{6}=+0.000000000\) \(a_{7}=-1.389661995\) \(a_{8}=+0.000000000\) \(a_{9}=+1.805053742\) \(a_{10}=+0.000000000\)
\(a_{11}=-1.014050176\) \(a_{12}=+0.000000000\) \(a_{13}=-0.274770011\) \(a_{14}=+0.000000000\) \(a_{15}=-2.348697661\)
\(a_{16}=+0.000000000\) \(a_{17}=+1.007382974\) \(a_{18}=+0.000000000\) \(a_{19}=+0.852067836\) \(a_{20}=+0.000000000\)
\(a_{21}=+2.327446857\) \(a_{22}=+0.000000000\) \(a_{23}=+0.825246426\) \(a_{24}=+0.000000000\) \(a_{25}=+0.966586458\)
\(a_{26}=+0.000000000\) \(a_{27}=-1.348327728\) \(a_{28}=+0.000000000\) \(a_{29}=+1.012130189\) \(a_{30}=+0.000000000\)
\(a_{31}=-0.019061343\) \(a_{32}=+0.000000000\) \(a_{33}=+1.698361108\) \(a_{34}=+0.000000000\) \(a_{35}=-1.948794010\)
\(a_{36}=+0.000000000\) \(a_{37}=-0.569017522\) \(a_{38}=+0.000000000\) \(a_{39}=+0.460155330\) \(a_{40}=+0.000000000\)
\(a_{41}=-0.314816901\) \(a_{42}=+0.000000000\) \(a_{43}=-0.491307898\) \(a_{44}=+0.000000000\) \(a_{45}=+2.527849118\)
\(a_{46}=+0.000000000\)

Showing all 46 available coefficients

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