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: \( 11.4110059735 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=-1.199685133\) \(a_{4}=+0.000000000\) \(a_{5}=+1.090550756\)
\(a_{6}=+0.000000000\) \(a_{7}=-1.744896646\) \(a_{8}=+0.000000000\) \(a_{9}=+0.439244418\) \(a_{10}=+0.000000000\)
\(a_{11}=-1.103322391\) \(a_{12}=+0.000000000\) \(a_{13}=+0.108501300\) \(a_{14}=+0.000000000\) \(a_{15}=-1.308317529\)
\(a_{16}=+0.000000000\) \(a_{17}=+0.824729527\) \(a_{18}=+0.000000000\) \(a_{19}=-0.089981116\) \(a_{20}=+0.000000000\)
\(a_{21}=+2.093326565\) \(a_{22}=+0.000000000\) \(a_{23}=+1.175680270\) \(a_{24}=+0.000000000\) \(a_{25}=+0.189300951\)
\(a_{26}=+0.000000000\) \(a_{27}=+0.672730135\) \(a_{28}=+0.000000000\) \(a_{29}=-0.590190796\) \(a_{30}=+0.000000000\)
\(a_{31}=+1.951331117\) \(a_{32}=+0.000000000\) \(a_{33}=+1.323639469\) \(a_{34}=+0.000000000\) \(a_{35}=-1.902898356\)
\(a_{36}=+0.000000000\) \(a_{37}=+0.198820425\) \(a_{38}=+0.000000000\) \(a_{39}=-0.130167381\) \(a_{40}=+0.000000000\)
\(a_{41}=+0.452207288\) \(a_{42}=+0.000000000\) \(a_{43}=+0.152542869\) \(a_{44}=+0.000000000\) \(a_{45}=+0.479018332\)
\(a_{46}=+0.000000000\) \(a_{47}=-1.012271495\) \(a_{48}=+0.000000000\) \(a_{49}=+2.044664305\) \(a_{50}=+0.000000000\)
\(a_{51}=-0.989415752\) \(a_{52}=+0.000000000\) \(a_{53}=-0.635104235\) \(a_{54}=+0.000000000\) \(a_{55}=-1.203229067\)
\(a_{56}=+0.000000000\) \(a_{57}=+0.107949007\) \(a_{58}=+0.000000000\) \(a_{59}=+1.083878691\) \(a_{60}=+0.000000000\)
\(a_{61}=+1.299819351\) \(a_{62}=+0.000000000\) \(a_{63}=-0.766436112\) \(a_{64}=+0.000000000\) \(a_{65}=+0.118326175\)
\(a_{66}=+0.000000000\) \(a_{67}=+0.999379649\) \(a_{68}=+0.000000000\) \(a_{69}=-1.410446140\) \(a_{70}=+0.000000000\)
\(a_{71}=-1.250509880\) \(a_{72}=+0.000000000\) \(a_{73}=+0.328377316\) \(a_{74}=+0.000000000\) \(a_{75}=-0.227101529\)
\(a_{76}=+0.000000000\) \(a_{77}=+1.925183543\) \(a_{78}=+0.000000000\) \(a_{79}=-0.623116635\) \(a_{80}=+0.000000000\)
\(a_{81}=-1.246308720\) \(a_{82}=+0.000000000\) \(a_{83}=+0.750492426\) \(a_{84}=+0.000000000\) \(a_{85}=+0.899409409\)
\(a_{86}=+0.000000000\) \(a_{87}=+0.708043124\) \(a_{88}=+0.000000000\) \(a_{89}=+0.162701547\) \(a_{90}=+0.000000000\)
\(a_{91}=-0.189323554\) \(a_{92}=+0.000000000\) \(a_{93}=-2.340982931\) \(a_{94}=+0.000000000\) \(a_{95}=-0.098128975\)
\(a_{96}=+0.000000000\) \(a_{97}=+0.123826316\) \(a_{98}=+0.000000000\) \(a_{99}=-0.484628203\) \(a_{100}=+0.000000000\)

Showing 100 of 1500 available coefficients

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