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: \( 9.81001812133 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=-1.684209361\) \(a_{4}=+0.000000000\) \(a_{5}=+1.128977462\)
\(a_{6}=+0.000000000\) \(a_{7}=+0.462244612\) \(a_{8}=+0.000000000\) \(a_{9}=+1.836561172\) \(a_{10}=+0.000000000\)
\(a_{11}=-1.145502223\) \(a_{12}=+0.000000000\) \(a_{13}=+0.959563503\) \(a_{14}=+0.000000000\) \(a_{15}=-1.901434410\)
\(a_{16}=+0.000000000\) \(a_{17}=-1.605761565\) \(a_{18}=+0.000000000\) \(a_{19}=-0.111309199\) \(a_{20}=+0.000000000\)
\(a_{21}=-0.778516703\) \(a_{22}=+0.000000000\) \(a_{23}=-0.098365329\) \(a_{24}=+0.000000000\) \(a_{25}=+0.274590110\)
\(a_{26}=+0.000000000\) \(a_{27}=-1.408944157\) \(a_{28}=+0.000000000\) \(a_{29}=+0.258809990\) \(a_{30}=+0.000000000\)
\(a_{31}=-0.926254690\) \(a_{32}=+0.000000000\) \(a_{33}=+1.929265567\) \(a_{34}=+0.000000000\) \(a_{35}=+0.521863749\)
\(a_{36}=+0.000000000\) \(a_{37}=-0.972284310\) \(a_{38}=+0.000000000\) \(a_{39}=-1.616105834\) \(a_{40}=+0.000000000\)
\(a_{41}=+0.545651300\) \(a_{42}=+0.000000000\) \(a_{43}=-0.061396200\) \(a_{44}=+0.000000000\) \(a_{45}=+2.073436171\)
\(a_{46}=+0.000000000\) \(a_{47}=-1.655000687\) \(a_{48}=+0.000000000\) \(a_{49}=-0.786329919\) \(a_{50}=+0.000000000\)
\(a_{51}=+2.704438660\) \(a_{52}=+0.000000000\) \(a_{53}=-0.600999832\) \(a_{54}=+0.000000000\) \(a_{55}=-1.293246192\)
\(a_{56}=+0.000000000\) \(a_{57}=+0.187467996\) \(a_{58}=+0.000000000\) \(a_{59}=-1.210000000\) \(a_{60}=+0.000000000\)

Showing all 60 available coefficients

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