Properties

Level $97$
Weight $0$
Character 97.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 97 \)
Weight: \( 0 \)
Character: 97.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 1.20940253 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.261283150\) \(a_{3}=+1.767305470\) \(a_{4}=-0.931731116\) \(a_{5}=-1.208918700\)
\(a_{6}=-0.461767140\) \(a_{7}=-0.458400600\) \(a_{8}=+0.504728791\) \(a_{9}=+2.123368624\) \(a_{10}=+0.315870086\)
\(a_{11}=+1.290907230\) \(a_{12}=-1.646653497\) \(a_{13}=+0.498960590\) \(a_{14}=+0.119772353\) \(a_{15}=-2.136528631\)
\(a_{16}=+0.799853987\) \(a_{17}=-1.512839590\) \(a_{18}=-0.554800443\) \(a_{19}=+0.701473930\) \(a_{20}=+1.126387169\)
\(a_{21}=-0.810133888\) \(a_{22}=-0.337292307\) \(a_{23}=+0.893817439\) \(a_{24}=+0.892009953\) \(a_{25}=+0.461484423\)
\(a_{26}=-0.130369995\) \(a_{27}=+1.985335515\) \(a_{28}=+0.427106102\) \(a_{29}=-1.562044965\) \(a_{30}=+0.558238931\)
\(a_{31}=+0.410280660\) \(a_{32}=-0.713717160\) \(a_{33}=+2.281427409\) \(a_{34}=+0.395279494\) \(a_{35}=+0.554169057\)
\(a_{36}=-1.978408617\) \(a_{37}=-0.023789835\) \(a_{38}=-0.183283318\) \(a_{39}=+0.881815780\) \(a_{40}=-0.610176074\)
\(a_{41}=-0.198435533\) \(a_{42}=+0.211674334\) \(a_{43}=+1.290199354\) \(a_{44}=-1.202778433\) \(a_{45}=-2.566980037\)
\(a_{46}=-0.233539436\) \(a_{47}=+0.486139631\) \(a_{48}=+1.413586327\) \(a_{49}=-0.789868890\) \(a_{50}=-0.120578104\)
\(a_{51}=-2.673649683\) \(a_{52}=-0.464897107\) \(a_{53}=-1.590946076\) \(a_{54}=-0.518734717\) \(a_{55}=-1.560601890\)
\(a_{56}=-0.231367981\) \(a_{57}=+1.239718714\) \(a_{58}=+0.408136029\) \(a_{59}=+0.834726452\) \(a_{60}=+1.990670205\)
\(a_{61}=+1.014403958\) \(a_{62}=-0.107199423\) \(a_{63}=-0.973353451\) \(a_{64}=-0.613371719\) \(a_{65}=-0.603202788\)
\(a_{66}=-0.596098540\) \(a_{67}=+0.897440537\) \(a_{68}=+1.409559719\) \(a_{69}=+1.579648450\) \(a_{70}=-0.144795037\)
\(a_{71}=-1.398077367\) \(a_{72}=+1.071725278\) \(a_{73}=+1.009341102\) \(a_{74}=+0.006215883\) \(a_{75}=+0.815583945\)
\(a_{76}=-0.653585087\) \(a_{77}=-0.591752649\) \(a_{78}=-0.230403605\) \(a_{79}=+0.351910733\) \(a_{80}=-0.966958442\)
\(a_{81}=+1.385325690\) \(a_{82}=+0.051847861\) \(a_{83}=-0.601080974\) \(a_{84}=+0.754826951\) \(a_{85}=+1.828900070\)
\(a_{86}=-0.337107351\) \(a_{87}=-2.760610612\) \(a_{88}=+0.651558045\) \(a_{89}=+0.474693815\) \(a_{90}=+0.670708630\)
\(a_{91}=-0.228723834\) \(a_{92}=-0.832797520\) \(a_{93}=+0.725091255\) \(a_{94}=-0.127020094\) \(a_{95}=-0.848024952\)
\(a_{96}=-1.261356241\) \(a_{97}=-0.101534616\) \(a_{98}=+0.206379432\) \(a_{99}=+2.741071909\) \(a_{100}=-0.429979396\)

Showing 100 of 546 available coefficients

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