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: \( 14.4102250052 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=+0.376695226\) \(a_{4}=+0.000000000\) \(a_{5}=-1.182264643\)
\(a_{6}=+0.000000000\) \(a_{7}=-1.770165034\) \(a_{8}=+0.000000000\) \(a_{9}=-0.858100707\) \(a_{10}=+0.000000000\)
\(a_{11}=+0.709309005\) \(a_{12}=+0.000000000\) \(a_{13}=-0.189514412\) \(a_{14}=+0.000000000\) \(a_{15}=-0.445353447\)
\(a_{16}=+0.000000000\) \(a_{17}=+1.346601981\) \(a_{18}=+0.000000000\) \(a_{19}=+0.468758120\) \(a_{20}=+0.000000000\)
\(a_{21}=-0.666812717\) \(a_{22}=+0.000000000\) \(a_{23}=-1.198933441\) \(a_{24}=+0.000000000\) \(a_{25}=+0.397749686\)
\(a_{26}=+0.000000000\) \(a_{27}=-0.699937665\) \(a_{28}=+0.000000000\) \(a_{29}=+0.299706087\) \(a_{30}=+0.000000000\)
\(a_{31}=+0.386940101\) \(a_{32}=+0.000000000\) \(a_{33}=+0.267193318\) \(a_{34}=+0.000000000\) \(a_{35}=+2.092803535\)
\(a_{36}=+0.000000000\) \(a_{37}=+1.841598827\) \(a_{38}=+0.000000000\) \(a_{39}=-0.071389209\) \(a_{40}=+0.000000000\)
\(a_{41}=-0.575548271\) \(a_{42}=+0.000000000\) \(a_{43}=+1.530364361\) \(a_{44}=+0.000000000\) \(a_{45}=+1.014500244\)
\(a_{46}=+0.000000000\) \(a_{47}=-1.200593562\) \(a_{48}=+0.000000000\) \(a_{49}=+2.133466707\) \(a_{50}=+0.000000000\)
\(a_{51}=+0.507199019\) \(a_{52}=+0.000000000\) \(a_{53}=-0.523311627\) \(a_{54}=+0.000000000\) \(a_{55}=-0.838820213\)
\(a_{56}=+0.000000000\) \(a_{57}=+0.175583285\) \(a_{58}=+0.000000000\) \(a_{59}=+0.498569593\) \(a_{60}=+0.000000000\)
\(a_{61}=-1.148011808\) \(a_{62}=+0.000000000\) \(a_{63}=+1.531370549\) \(a_{64}=+0.000000000\) \(a_{65}=+0.256376101\)
\(a_{66}=+0.000000000\)

Showing all 66 available coefficients

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