Properties

Level $8$
Weight $0$
Character 8.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 8 = 2^{3} \)
Weight: \( 0 \)
Character: 8.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 7.74444773702 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=-0.399815561\) \(a_{4}=+0.000000000\) \(a_{5}=+1.154388782\)
\(a_{6}=+0.000000000\) \(a_{7}=-0.779044103\) \(a_{8}=+0.000000000\) \(a_{9}=-0.840147517\) \(a_{10}=+0.000000000\)
\(a_{11}=-0.859664889\) \(a_{12}=+0.000000000\) \(a_{13}=-1.377048541\) \(a_{14}=+0.000000000\) \(a_{15}=-0.461542598\)
\(a_{16}=+0.000000000\) \(a_{17}=+1.446276223\) \(a_{18}=+0.000000000\) \(a_{19}=-1.424886052\) \(a_{20}=+0.000000000\)
\(a_{21}=+0.311473955\) \(a_{22}=+0.000000000\) \(a_{23}=-0.885029132\) \(a_{24}=+0.000000000\) \(a_{25}=+0.332613459\)
\(a_{26}=+0.000000000\) \(a_{27}=+0.735719612\) \(a_{28}=+0.000000000\) \(a_{29}=+0.543756740\) \(a_{30}=+0.000000000\)
\(a_{31}=-0.950222000\) \(a_{32}=+0.000000000\) \(a_{33}=+0.343707400\) \(a_{34}=+0.000000000\) \(a_{35}=-0.899319773\)
\(a_{36}=+0.000000000\) \(a_{37}=-0.469805000\) \(a_{38}=+0.000000000\) \(a_{39}=+0.550565435\) \(a_{40}=+0.000000000\)
\(a_{41}=+1.070250034\) \(a_{42}=+0.000000000\) \(a_{43}=+0.720299721\) \(a_{44}=+0.000000000\) \(a_{45}=-0.969856869\)
\(a_{46}=+0.000000000\) \(a_{47}=-0.062999964\) \(a_{48}=+0.000000000\) \(a_{49}=-0.393090285\) \(a_{50}=+0.000000000\)
\(a_{51}=-0.578243739\) \(a_{52}=+0.000000000\)

Showing all 52 available coefficients

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