Properties

Level $8$
Weight $0$
Character 8.1
Symmetry even
Fricke sign $+1$

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 8 = 2^{3} \)
Weight: \( 0 \)
Character: 8.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 7.22656906706 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=-1.537111904\) \(a_{4}=+0.000000000\) \(a_{5}=-1.006424888\)
\(a_{6}=+0.000000000\) \(a_{7}=+1.143187166\) \(a_{8}=+0.000000000\) \(a_{9}=+1.362713005\) \(a_{10}=+0.000000000\)
\(a_{11}=+0.816976768\) \(a_{12}=+0.000000000\) \(a_{13}=-0.788866710\) \(a_{14}=+0.000000000\) \(a_{15}=+1.546987675\)
\(a_{16}=+0.000000000\) \(a_{17}=+0.298894811\) \(a_{18}=+0.000000000\) \(a_{19}=-0.312809533\) \(a_{20}=+0.000000000\)
\(a_{21}=-1.757206601\) \(a_{22}=+0.000000000\) \(a_{23}=+1.869289237\) \(a_{24}=+0.000000000\) \(a_{25}=+0.012891055\)
\(a_{26}=+0.000000000\) \(a_{27}=-0.557530477\) \(a_{28}=+0.000000000\) \(a_{29}=+0.649917900\) \(a_{30}=+0.000000000\)
\(a_{31}=+0.459818793\) \(a_{32}=+0.000000000\) \(a_{33}=-1.255784714\) \(a_{34}=+0.000000000\) \(a_{35}=-1.150532029\)
\(a_{36}=+0.000000000\) \(a_{37}=+0.748932871\) \(a_{38}=+0.000000000\) \(a_{39}=+1.212576410\) \(a_{40}=+0.000000000\)
\(a_{41}=+0.281448933\) \(a_{42}=+0.000000000\) \(a_{43}=+0.713802161\) \(a_{44}=+0.000000000\) \(a_{45}=-1.371468283\)
\(a_{46}=+0.000000000\) \(a_{47}=-0.742913379\) \(a_{48}=+0.000000000\) \(a_{49}=+0.306876897\) \(a_{50}=+0.000000000\)
\(a_{51}=-0.459434772\) \(a_{52}=+0.000000000\) \(a_{53}=+0.922015684\) \(a_{54}=+0.000000000\) \(a_{55}=-0.822225752\)
\(a_{56}=+0.000000000\) \(a_{57}=+0.480823256\) \(a_{58}=+0.000000000\) \(a_{59}=+0.948052755\) \(a_{60}=+0.000000000\)
\(a_{61}=-0.960123060\) \(a_{62}=+0.000000000\) \(a_{63}=+1.557836018\) \(a_{64}=+0.000000000\) \(a_{65}=+0.793935090\)
\(a_{66}=+0.000000000\) \(a_{67}=-1.449391408\) \(a_{68}=+0.000000000\) \(a_{69}=-2.873306738\) \(a_{70}=+0.000000000\)
\(a_{71}=-0.098454330\) \(a_{72}=+0.000000000\) \(a_{73}=+1.925935312\) \(a_{74}=+0.000000000\) \(a_{75}=-0.019814993\)
\(a_{76}=+0.000000000\) \(a_{77}=+0.933957357\) \(a_{78}=+0.000000000\) \(a_{79}=+0.089310944\) \(a_{80}=+0.000000000\)
\(a_{81}=-0.505726272\) \(a_{82}=+0.000000000\) \(a_{83}=+0.893080987\) \(a_{84}=+0.000000000\) \(a_{85}=-0.300815176\)
\(a_{86}=+0.000000000\) \(a_{87}=-0.998996541\) \(a_{88}=+0.000000000\) \(a_{89}=+1.417443131\) \(a_{90}=+0.000000000\)
\(a_{91}=-0.901822298\) \(a_{92}=+0.000000000\) \(a_{93}=-0.706792939\) \(a_{94}=+0.000000000\) \(a_{95}=+0.314819299\)
\(a_{96}=+0.000000000\) \(a_{97}=-1.528304336\) \(a_{98}=+0.000000000\) \(a_{99}=+1.113304866\) \(a_{100}=+0.000000000\)

Showing 100 of 1500 available coefficients

Rows: Cols: