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: \( 6.22318082532 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=+0.496646444\) \(a_{4}=+0.000000000\) \(a_{5}=-1.431283418\)
\(a_{6}=+0.000000000\) \(a_{7}=-0.599453768\) \(a_{8}=+0.000000000\) \(a_{9}=-0.753342310\) \(a_{10}=+0.000000000\)
\(a_{11}=-1.256676368\) \(a_{12}=+0.000000000\) \(a_{13}=+1.549056547\) \(a_{14}=+0.000000000\) \(a_{15}=-0.710841820\)
\(a_{16}=+0.000000000\) \(a_{17}=+0.048494310\) \(a_{18}=+0.000000000\) \(a_{19}=-0.597447269\) \(a_{20}=+0.000000000\)
\(a_{21}=-0.297716582\) \(a_{22}=+0.000000000\) \(a_{23}=+0.763186664\) \(a_{24}=+0.000000000\) \(a_{25}=+1.048572222\)
\(a_{26}=+0.000000000\) \(a_{27}=-0.870791223\) \(a_{28}=+0.000000000\) \(a_{29}=-0.099152685\) \(a_{30}=+0.000000000\)
\(a_{31}=-0.649361467\) \(a_{32}=+0.000000000\) \(a_{33}=-0.624123847\) \(a_{34}=+0.000000000\) \(a_{35}=+0.857988238\)
\(a_{36}=+0.000000000\) \(a_{37}=+0.657117439\) \(a_{38}=+0.000000000\) \(a_{39}=+0.769333425\) \(a_{40}=+0.000000000\)
\(a_{41}=-0.963842936\) \(a_{42}=+0.000000000\) \(a_{43}=-0.233365429\) \(a_{44}=+0.000000000\) \(a_{45}=+1.078246356\)
\(a_{46}=+0.000000000\) \(a_{47}=-1.641546487\) \(a_{48}=+0.000000000\) \(a_{49}=-0.640655180\) \(a_{50}=+0.000000000\)
\(a_{51}=+0.024084527\) \(a_{52}=+0.000000000\) \(a_{53}=+0.714295337\) \(a_{54}=+0.000000000\) \(a_{55}=+1.798660047\)
\(a_{56}=+0.000000000\) \(a_{57}=-0.296720062\) \(a_{58}=+0.000000000\) \(a_{59}=-0.882205850\) \(a_{60}=+0.000000000\)
\(a_{61}=+0.667477181\) \(a_{62}=+0.000000000\) \(a_{63}=+0.451593887\) \(a_{64}=+0.000000000\) \(a_{65}=-2.217138950\)
\(a_{66}=+0.000000000\) \(a_{67}=+0.268486308\) \(a_{68}=+0.000000000\) \(a_{69}=+0.379033944\) \(a_{70}=+0.000000000\)
\(a_{71}=-1.173775695\) \(a_{72}=+0.000000000\) \(a_{73}=+1.010570639\) \(a_{74}=+0.000000000\) \(a_{75}=+0.520769666\)
\(a_{76}=+0.000000000\) \(a_{77}=+0.753319384\) \(a_{78}=+0.000000000\) \(a_{79}=-0.554326257\) \(a_{80}=+0.000000000\)
\(a_{81}=+0.320866946\) \(a_{82}=+0.000000000\) \(a_{83}=+0.711784477\) \(a_{84}=+0.000000000\) \(a_{85}=-0.069409102\)
\(a_{86}=+0.000000000\) \(a_{87}=-0.049243829\) \(a_{88}=+0.000000000\) \(a_{89}=-1.681402698\) \(a_{90}=+0.000000000\)
\(a_{91}=-0.928587785\) \(a_{92}=+0.000000000\) \(a_{93}=-0.322503062\) \(a_{94}=+0.000000000\) \(a_{95}=+0.855116370\)
\(a_{96}=+0.000000000\) \(a_{97}=+0.301367908\) \(a_{98}=+0.000000000\) \(a_{99}=+0.946707478\) \(a_{100}=+0.000000000\)

Showing 100 of 1500 available coefficients

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