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: \( 9.9039777038 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=-1.172137929\) \(a_{4}=+0.000000000\) \(a_{5}=+0.685449050\)
\(a_{6}=+0.000000000\) \(a_{7}=+0.573348122\) \(a_{8}=+0.000000000\) \(a_{9}=+0.373907326\) \(a_{10}=+0.000000000\)
\(a_{11}=+1.633562152\) \(a_{12}=+0.000000000\) \(a_{13}=-1.903960620\) \(a_{14}=+0.000000000\) \(a_{15}=-0.803440830\)
\(a_{16}=+0.000000000\) \(a_{17}=-0.402182035\) \(a_{18}=+0.000000000\) \(a_{19}=-1.222370850\) \(a_{20}=+0.000000000\)
\(a_{21}=-0.672043081\) \(a_{22}=+0.000000000\) \(a_{23}=-0.658079336\) \(a_{24}=+0.000000000\) \(a_{25}=-0.530159600\)
\(a_{26}=+0.000000000\) \(a_{27}=+0.733866971\) \(a_{28}=+0.000000000\) \(a_{29}=+0.059257501\) \(a_{30}=+0.000000000\)
\(a_{31}=+0.388919802\) \(a_{32}=+0.000000000\) \(a_{33}=-1.914760176\) \(a_{34}=+0.000000000\) \(a_{35}=+0.393000975\)
\(a_{36}=+0.000000000\) \(a_{37}=-0.647883394\) \(a_{38}=+0.000000000\) \(a_{39}=+2.231704459\) \(a_{40}=+0.000000000\)
\(a_{41}=+0.014173438\) \(a_{42}=+0.000000000\) \(a_{43}=-1.297396953\) \(a_{44}=+0.000000000\) \(a_{45}=+0.256294421\)
\(a_{46}=+0.000000000\) \(a_{47}=+0.130746489\) \(a_{48}=+0.000000000\) \(a_{49}=-0.671271931\) \(a_{50}=+0.000000000\)
\(a_{51}=+0.471412818\) \(a_{52}=+0.000000000\) \(a_{53}=-1.461527868\) \(a_{54}=+0.000000000\) \(a_{55}=+1.119723624\)
\(a_{56}=+0.000000000\) \(a_{57}=+1.432787237\) \(a_{58}=+0.000000000\) \(a_{59}=-0.391350932\) \(a_{60}=+0.000000000\)
\(a_{61}=+0.198467267\) \(a_{62}=+0.000000000\) \(a_{63}=+0.214379064\) \(a_{64}=+0.000000000\) \(a_{65}=-1.305067999\)
\(a_{66}=+0.000000000\) \(a_{67}=-1.512923534\) \(a_{68}=+0.000000000\) \(a_{69}=+0.771359744\) \(a_{70}=+0.000000000\)
\(a_{71}=+0.567761350\) \(a_{72}=+0.000000000\) \(a_{73}=-0.066725331\) \(a_{74}=+0.000000000\) \(a_{75}=+0.621420077\)
\(a_{76}=+0.000000000\) \(a_{77}=+0.936599792\) \(a_{78}=+0.000000000\) \(a_{79}=-0.197316210\) \(a_{80}=+0.000000000\)
\(a_{81}=-1.234100637\) \(a_{82}=+0.000000000\) \(a_{83}=+0.993793737\) \(a_{84}=+0.000000000\) \(a_{85}=-0.275675294\)
\(a_{86}=+0.000000000\) \(a_{87}=-0.069457965\) \(a_{88}=+0.000000000\) \(a_{89}=-0.016407037\) \(a_{90}=+0.000000000\)
\(a_{91}=-1.091632246\) \(a_{92}=+0.000000000\) \(a_{93}=-0.455867647\) \(a_{94}=+0.000000000\) \(a_{95}=-0.837872937\)
\(a_{96}=+0.000000000\) \(a_{97}=+1.361654220\) \(a_{98}=+0.000000000\) \(a_{99}=+0.610800853\) \(a_{100}=+0.000000000\)

Showing 100 of 1500 available coefficients

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