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: \( 11.4536636942 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=+1.746137996\) \(a_{4}=+0.000000000\) \(a_{5}=+0.507914187\)
\(a_{6}=+0.000000000\) \(a_{7}=+1.219385687\) \(a_{8}=+0.000000000\) \(a_{9}=+2.048997903\) \(a_{10}=+0.000000000\)
\(a_{11}=+0.388612546\) \(a_{12}=+0.000000000\) \(a_{13}=-1.194276954\) \(a_{14}=+0.000000000\) \(a_{15}=+0.886888261\)
\(a_{16}=+0.000000000\) \(a_{17}=-1.438607366\) \(a_{18}=+0.000000000\) \(a_{19}=+1.107645312\) \(a_{20}=+0.000000000\)
\(a_{21}=+2.129215680\) \(a_{22}=+0.000000000\) \(a_{23}=+1.023084185\) \(a_{24}=+0.000000000\) \(a_{25}=-0.742023179\)
\(a_{26}=+0.000000000\) \(a_{27}=+1.831695096\) \(a_{28}=+0.000000000\) \(a_{29}=+0.220508300\) \(a_{30}=+0.000000000\)
\(a_{31}=+0.144290699\) \(a_{32}=+0.000000000\) \(a_{33}=+0.678571150\) \(a_{34}=+0.000000000\) \(a_{35}=+0.619343353\)
\(a_{36}=+0.000000000\) \(a_{37}=+0.185982994\) \(a_{38}=+0.000000000\) \(a_{39}=-2.085371568\) \(a_{40}=+0.000000000\)
\(a_{41}=+0.685096360\) \(a_{42}=+0.000000000\) \(a_{43}=+0.423575234\) \(a_{44}=+0.000000000\) \(a_{45}=+1.040743114\)
\(a_{46}=+0.000000000\) \(a_{47}=+0.287907572\) \(a_{48}=+0.000000000\) \(a_{49}=+0.487134637\) \(a_{50}=+0.000000000\)
\(a_{51}=-2.511329161\) \(a_{52}=+0.000000000\) \(a_{53}=+0.084653006\) \(a_{54}=+0.000000000\) \(a_{55}=+0.202287656\)
\(a_{56}=+0.000000000\) \(a_{57}=+1.942983012\) \(a_{58}=+0.000000000\) \(a_{59}=-1.423668967\) \(a_{60}=+0.000000000\)

Showing all 60 available coefficients

Rows: Cols: