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: \( 12.9167943228 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=-0.405465771\) \(a_{4}=+0.000000000\) \(a_{5}=+1.653393658\)
\(a_{6}=+0.000000000\) \(a_{7}=+1.785565825\) \(a_{8}=+0.000000000\) \(a_{9}=-0.835597508\) \(a_{10}=+0.000000000\)
\(a_{11}=-0.308693376\) \(a_{12}=+0.000000000\) \(a_{13}=+0.870978179\) \(a_{14}=+0.000000000\) \(a_{15}=-0.670394535\)
\(a_{16}=+0.000000000\) \(a_{17}=+0.119738763\) \(a_{18}=+0.000000000\) \(a_{19}=-0.895637192\) \(a_{20}=+0.000000000\)
\(a_{21}=-0.723985825\) \(a_{22}=+0.000000000\) \(a_{23}=+0.191330246\) \(a_{24}=+0.000000000\) \(a_{25}=+1.733710588\)
\(a_{26}=+0.000000000\) \(a_{27}=+0.744271960\) \(a_{28}=+0.000000000\) \(a_{29}=+1.369859944\) \(a_{30}=+0.000000000\)
\(a_{31}=-0.223254171\) \(a_{32}=+0.000000000\) \(a_{33}=+0.125164598\) \(a_{34}=+0.000000000\) \(a_{35}=+2.952243211\)
\(a_{36}=+0.000000000\) \(a_{37}=-0.408190601\) \(a_{38}=+0.000000000\) \(a_{39}=-0.353151839\) \(a_{40}=+0.000000000\)
\(a_{41}=+1.088013106\) \(a_{42}=+0.000000000\) \(a_{43}=+0.058810549\) \(a_{44}=+0.000000000\) \(a_{45}=-1.381571595\)
\(a_{46}=+0.000000000\) \(a_{47}=-0.150720042\) \(a_{48}=+0.000000000\) \(a_{49}=+2.188245316\) \(a_{50}=+0.000000000\)
\(a_{51}=-0.048549970\) \(a_{52}=+0.000000000\) \(a_{53}=-0.110652674\) \(a_{54}=+0.000000000\) \(a_{55}=-0.510391670\)
\(a_{56}=+0.000000000\) \(a_{57}=+0.363150225\) \(a_{58}=+0.000000000\) \(a_{59}=-1.422793280\) \(a_{60}=+0.000000000\)
\(a_{61}=+0.988203607\) \(a_{62}=+0.000000000\) \(a_{63}=-1.492014354\) \(a_{64}=+0.000000000\) \(a_{65}=+1.440069797\)
\(a_{66}=+0.000000000\) \(a_{67}=+0.866683801\) \(a_{68}=+0.000000000\) \(a_{69}=-0.077577866\) \(a_{70}=+0.000000000\)
\(a_{71}=-0.154869283\) \(a_{72}=+0.000000000\) \(a_{73}=+0.156343790\) \(a_{74}=+0.000000000\) \(a_{75}=-0.702960301\)
\(a_{76}=+0.000000000\) \(a_{77}=-0.551192342\) \(a_{78}=+0.000000000\) \(a_{79}=-0.072179137\) \(a_{80}=+0.000000000\)
\(a_{81}=+0.533820705\) \(a_{82}=+0.000000000\) \(a_{83}=-0.688900644\) \(a_{84}=+0.000000000\) \(a_{85}=+0.197975309\)
\(a_{86}=+0.000000000\) \(a_{87}=-0.555431321\) \(a_{88}=+0.000000000\) \(a_{89}=+1.575783754\) \(a_{90}=+0.000000000\)
\(a_{91}=+1.555188871\) \(a_{92}=+0.000000000\) \(a_{93}=+0.090521925\) \(a_{94}=+0.000000000\) \(a_{95}=-1.480840854\)
\(a_{96}=+0.000000000\) \(a_{97}=-1.803525622\) \(a_{98}=+0.000000000\) \(a_{99}=+0.257943416\) \(a_{100}=+0.000000000\)

Showing 100 of 1500 available coefficients

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