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: \( 13.5200506514 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=+1.537565813\) \(a_{4}=+0.000000000\) \(a_{5}=+1.484753908\)
\(a_{6}=+0.000000000\) \(a_{7}=+0.475042119\) \(a_{8}=+0.000000000\) \(a_{9}=+1.364108629\) \(a_{10}=+0.000000000\)
\(a_{11}=+1.520376338\) \(a_{12}=+0.000000000\) \(a_{13}=-0.103197511\) \(a_{14}=+0.000000000\) \(a_{15}=+2.282906849\)
\(a_{16}=+0.000000000\) \(a_{17}=-0.290000016\) \(a_{18}=+0.000000000\) \(a_{19}=-1.512851491\) \(a_{20}=+0.000000000\)
\(a_{21}=+0.730408522\) \(a_{22}=+0.000000000\) \(a_{23}=-1.583718782\) \(a_{24}=+0.000000000\) \(a_{25}=+1.204494166\)
\(a_{26}=+0.000000000\) \(a_{27}=+0.559840981\) \(a_{28}=+0.000000000\) \(a_{29}=-0.070880295\) \(a_{30}=+0.000000000\)
\(a_{31}=+1.227067036\) \(a_{32}=+0.000000000\) \(a_{33}=+2.337678681\) \(a_{34}=+0.000000000\) \(a_{35}=+0.705320643\)
\(a_{36}=+0.000000000\) \(a_{37}=-0.185259132\) \(a_{38}=+0.000000000\) \(a_{39}=-0.158672964\) \(a_{40}=+0.000000000\)
\(a_{41}=+0.756648820\) \(a_{42}=+0.000000000\) \(a_{43}=+0.110790440\) \(a_{44}=+0.000000000\) \(a_{45}=+2.025365608\)
\(a_{46}=+0.000000000\) \(a_{47}=-0.227654265\) \(a_{48}=+0.000000000\) \(a_{49}=-0.774334985\) \(a_{50}=+0.000000000\)
\(a_{51}=-0.445894110\) \(a_{52}=+0.000000000\) \(a_{53}=-0.200060347\) \(a_{54}=+0.000000000\) \(a_{55}=+2.257384709\)
\(a_{56}=+0.000000000\) \(a_{57}=-2.326108733\) \(a_{58}=+0.000000000\) \(a_{59}=-0.194638424\) \(a_{60}=+0.000000000\)
\(a_{61}=+1.449090341\) \(a_{62}=+0.000000000\) \(a_{63}=+0.648009054\) \(a_{64}=+0.000000000\) \(a_{65}=-0.153222907\)
\(a_{66}=+0.000000000\) \(a_{67}=+1.114146800\) \(a_{68}=+0.000000000\) \(a_{69}=-2.435071857\) \(a_{70}=+0.000000000\)
\(a_{71}=-0.826834851\) \(a_{72}=+0.000000000\) \(a_{73}=-0.550378363\) \(a_{74}=+0.000000000\) \(a_{75}=+1.851989052\)
\(a_{76}=+0.000000000\) \(a_{77}=+0.722242798\) \(a_{78}=+0.000000000\) \(a_{79}=-0.061218360\) \(a_{80}=+0.000000000\)
\(a_{81}=-0.503316277\) \(a_{82}=+0.000000000\) \(a_{83}=+1.024143014\) \(a_{84}=+0.000000000\) \(a_{85}=-0.430578667\)
\(a_{86}=+0.000000000\) \(a_{87}=-0.108983106\) \(a_{88}=+0.000000000\) \(a_{89}=-1.335255276\) \(a_{90}=+0.000000000\)
\(a_{91}=-0.049023164\) \(a_{92}=+0.000000000\) \(a_{93}=+1.886696325\) \(a_{94}=+0.000000000\) \(a_{95}=-2.246212164\)
\(a_{96}=+0.000000000\) \(a_{97}=+0.002087439\) \(a_{98}=+0.000000000\) \(a_{99}=+2.073958483\) \(a_{100}=+0.000000000\)

Showing 100 of 1500 available coefficients

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