Properties

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

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Maass form invariants

Level: \( 8 = 2^{3} \)
Weight: \( 0 \)
Character: 8.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 12.9838454746 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=-0.591068917\) \(a_{4}=+0.000000000\) \(a_{5}=-0.617072556\)
\(a_{6}=+0.000000000\) \(a_{7}=-0.097902599\) \(a_{8}=+0.000000000\) \(a_{9}=-0.650637535\) \(a_{10}=+0.000000000\)
\(a_{11}=-1.094181954\) \(a_{12}=+0.000000000\) \(a_{13}=+0.739756184\) \(a_{14}=+0.000000000\) \(a_{15}=+0.364732408\)
\(a_{16}=+0.000000000\) \(a_{17}=-0.967876259\) \(a_{18}=+0.000000000\) \(a_{19}=-1.096632337\) \(a_{20}=+0.000000000\)
\(a_{21}=+0.057867183\) \(a_{22}=+0.000000000\) \(a_{23}=+1.174574916\) \(a_{24}=+0.000000000\) \(a_{25}=-0.619221460\)
\(a_{26}=+0.000000000\) \(a_{27}=+0.975640541\) \(a_{28}=+0.000000000\) \(a_{29}=+1.593702941\) \(a_{30}=+0.000000000\)
\(a_{31}=+1.404911339\) \(a_{32}=+0.000000000\) \(a_{33}=+0.646736944\) \(a_{34}=+0.000000000\) \(a_{35}=+0.060413015\)
\(a_{36}=+0.000000000\) \(a_{37}=+0.508520837\) \(a_{38}=+0.000000000\) \(a_{39}=-0.437246793\) \(a_{40}=+0.000000000\)
\(a_{41}=+1.244184602\) \(a_{42}=+0.000000000\) \(a_{43}=+0.218884557\) \(a_{44}=+0.000000000\) \(a_{45}=+0.401495082\)
\(a_{46}=+0.000000000\) \(a_{47}=+0.410314713\) \(a_{48}=+0.000000000\) \(a_{49}=-0.990382519\) \(a_{50}=+0.000000000\)
\(a_{51}=+0.572118007\) \(a_{52}=+0.000000000\) \(a_{53}=-1.639499959\) \(a_{54}=+0.000000000\) \(a_{55}=+0.675146390\)
\(a_{56}=+0.000000000\) \(a_{57}=+0.649199834\) \(a_{58}=+0.000000000\) \(a_{59}=+1.453534567\) \(a_{60}=+0.000000000\)
\(a_{61}=-0.780574992\) \(a_{62}=+0.000000000\) \(a_{63}=+0.118231914\) \(a_{64}=+0.000000000\) \(a_{65}=-0.248127221\)

Showing all 65 available coefficients

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