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: \( 11.1062703875 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=+0.433118611\) \(a_{4}=+0.000000000\) \(a_{5}=+0.066217592\)
\(a_{6}=+0.000000000\) \(a_{7}=-0.288576466\) \(a_{8}=+0.000000000\) \(a_{9}=-0.812408269\) \(a_{10}=+0.000000000\)
\(a_{11}=-0.047661323\) \(a_{12}=+0.000000000\) \(a_{13}=+1.439103396\) \(a_{14}=+0.000000000\) \(a_{15}=+0.028680072\)
\(a_{16}=+0.000000000\) \(a_{17}=-1.351445419\) \(a_{18}=+0.000000000\) \(a_{19}=-0.730328964\) \(a_{20}=+0.000000000\)
\(a_{21}=-0.124987838\) \(a_{22}=+0.000000000\) \(a_{23}=-1.666025488\) \(a_{24}=+0.000000000\) \(a_{25}=-0.995615230\)
\(a_{26}=+0.000000000\) \(a_{27}=-0.784987752\) \(a_{28}=+0.000000000\) \(a_{29}=+0.326352335\) \(a_{30}=+0.000000000\)
\(a_{31}=-0.057328834\) \(a_{32}=+0.000000000\) \(a_{33}=-0.020643006\) \(a_{34}=+0.000000000\) \(a_{35}=-0.019108838\)
\(a_{36}=+0.000000000\) \(a_{37}=-1.397620521\) \(a_{38}=+0.000000000\) \(a_{39}=+0.623302461\) \(a_{40}=+0.000000000\)
\(a_{41}=-0.973890233\) \(a_{42}=+0.000000000\) \(a_{43}=+1.671497907\) \(a_{44}=+0.000000000\) \(a_{45}=-0.053795720\)
\(a_{46}=+0.000000000\) \(a_{47}=+0.502510413\) \(a_{48}=+0.000000000\) \(a_{49}=-0.916723624\) \(a_{50}=+0.000000000\)
\(a_{51}=-0.585336162\) \(a_{52}=+0.000000000\) \(a_{53}=-0.130264810\) \(a_{54}=+0.000000000\) \(a_{55}=-0.003156018\)
\(a_{56}=+0.000000000\) \(a_{57}=-0.316319066\) \(a_{58}=+0.000000000\) \(a_{59}=+1.587446128\) \(a_{60}=+0.000000000\)
\(a_{61}=-0.453412380\) \(a_{62}=+0.000000000\) \(a_{63}=+0.234441907\) \(a_{64}=+0.000000000\) \(a_{65}=+0.095293962\)
\(a_{66}=+0.000000000\) \(a_{67}=+0.388969431\) \(a_{68}=+0.000000000\) \(a_{69}=-0.721586645\) \(a_{70}=+0.000000000\)
\(a_{71}=-1.384526047\) \(a_{72}=+0.000000000\) \(a_{73}=+0.605596989\) \(a_{74}=+0.000000000\) \(a_{75}=-0.431219486\)
\(a_{76}=+0.000000000\) \(a_{77}=+0.013753937\) \(a_{78}=+0.000000000\) \(a_{79}=+1.067758391\) \(a_{80}=+0.000000000\)
\(a_{81}=+0.472415464\) \(a_{82}=+0.000000000\) \(a_{83}=+0.427181408\) \(a_{84}=+0.000000000\) \(a_{85}=-0.089489457\)
\(a_{86}=+0.000000000\) \(a_{87}=+0.141349270\) \(a_{88}=+0.000000000\) \(a_{89}=-1.022408735\) \(a_{90}=+0.000000000\)
\(a_{91}=-0.415291372\) \(a_{92}=+0.000000000\) \(a_{93}=-0.024830185\) \(a_{94}=+0.000000000\) \(a_{95}=-0.048360626\)
\(a_{96}=+0.000000000\) \(a_{97}=-0.712750888\) \(a_{98}=+0.000000000\) \(a_{99}=+0.038720452\) \(a_{100}=+0.000000000\)

Showing 100 of 1500 available coefficients

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