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: \( 12.4144645265 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=+0.928181522\) \(a_{4}=+0.000000000\) \(a_{5}=+0.486666316\)
\(a_{6}=+0.000000000\) \(a_{7}=-0.775022887\) \(a_{8}=+0.000000000\) \(a_{9}=-0.138479062\) \(a_{10}=+0.000000000\)
\(a_{11}=-1.651936753\) \(a_{12}=+0.000000000\) \(a_{13}=+0.047928141\) \(a_{14}=+0.000000000\) \(a_{15}=+0.451714682\)
\(a_{16}=+0.000000000\) \(a_{17}=-0.182606609\) \(a_{18}=+0.000000000\) \(a_{19}=+1.662885726\) \(a_{20}=+0.000000000\)
\(a_{21}=-0.719361923\) \(a_{22}=+0.000000000\) \(a_{23}=-1.498438107\) \(a_{24}=+0.000000000\) \(a_{25}=-0.763155897\)
\(a_{26}=+0.000000000\) \(a_{27}=-1.056715229\) \(a_{28}=+0.000000000\) \(a_{29}=-0.875926268\) \(a_{30}=+0.000000000\)
\(a_{31}=+0.356165259\) \(a_{32}=+0.000000000\) \(a_{33}=-1.533297170\) \(a_{34}=+0.000000000\) \(a_{35}=-0.377177533\)
\(a_{36}=+0.000000000\) \(a_{37}=-1.093987479\) \(a_{38}=+0.000000000\) \(a_{39}=+0.044486014\) \(a_{40}=+0.000000000\)
\(a_{41}=+1.446860955\) \(a_{42}=+0.000000000\) \(a_{43}=-0.388649662\) \(a_{44}=+0.000000000\) \(a_{45}=-0.067393095\)
\(a_{46}=+0.000000000\) \(a_{47}=-1.013766338\) \(a_{48}=+0.000000000\) \(a_{49}=-0.399339525\) \(a_{50}=+0.000000000\)
\(a_{51}=-0.169492080\) \(a_{52}=+0.000000000\) \(a_{53}=+1.188926685\) \(a_{54}=+0.000000000\) \(a_{55}=-0.803941974\)
\(a_{56}=+0.000000000\) \(a_{57}=+1.543459805\) \(a_{58}=+0.000000000\) \(a_{59}=-1.257452259\) \(a_{60}=+0.000000000\)
\(a_{61}=+0.627514487\) \(a_{62}=+0.000000000\) \(a_{63}=+0.107324442\) \(a_{64}=+0.000000000\) \(a_{65}=+0.023325012\)
\(a_{66}=+0.000000000\) \(a_{67}=-1.203905166\) \(a_{68}=+0.000000000\) \(a_{69}=-1.390822563\) \(a_{70}=+0.000000000\)
\(a_{71}=+1.127309224\) \(a_{72}=+0.000000000\) \(a_{73}=+1.450638915\) \(a_{74}=+0.000000000\) \(a_{75}=-0.708347202\)
\(a_{76}=+0.000000000\) \(a_{77}=+1.280288791\) \(a_{78}=+0.000000000\) \(a_{79}=+0.196677751\) \(a_{80}=+0.000000000\)
\(a_{81}=-0.842344486\) \(a_{82}=+0.000000000\) \(a_{83}=-0.574654574\) \(a_{84}=+0.000000000\) \(a_{85}=-0.088868492\)
\(a_{86}=+0.000000000\) \(a_{87}=-0.813018573\) \(a_{88}=+0.000000000\) \(a_{89}=+0.263209581\) \(a_{90}=+0.000000000\)
\(a_{91}=-0.037145406\) \(a_{92}=+0.000000000\) \(a_{93}=+0.330586012\) \(a_{94}=+0.000000000\) \(a_{95}=+0.809270471\)
\(a_{96}=+0.000000000\) \(a_{97}=-0.611534299\) \(a_{98}=+0.000000000\) \(a_{99}=+0.228758652\) \(a_{100}=+0.000000000\)

Showing 100 of 1500 available coefficients

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