Properties

Level $89$
Weight $0$
Character 89.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 89 \)
Weight: \( 0 \)
Character: 89.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 0.48943598 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.580384140\) \(a_{3}=-1.725291758\) \(a_{4}=-0.663154250\) \(a_{5}=+0.110907885\)
\(a_{6}=-1.001331973\) \(a_{7}=-0.044286325\) \(a_{8}=-0.965268349\) \(a_{9}=+1.976631650\) \(a_{10}=+0.064369178\)
\(a_{11}=-0.299113892\) \(a_{12}=+1.144134562\) \(a_{13}=-0.142346739\) \(a_{14}=-0.025703081\) \(a_{15}=-0.191348461\)
\(a_{16}=+0.102927809\) \(a_{17}=+1.176709005\) \(a_{18}=+1.147205660\) \(a_{19}=+0.464705201\) \(a_{20}=-0.073549036\)
\(a_{21}=+0.076406832\) \(a_{22}=-0.173600959\) \(a_{23}=-1.476549210\) \(a_{24}=+1.665369527\) \(a_{25}=-0.987699441\)
\(a_{26}=-0.082615789\) \(a_{27}=-1.684974537\) \(a_{28}=+0.029368665\) \(a_{29}=-0.259043217\) \(a_{30}=-0.111055612\)
\(a_{31}=-0.820754093\) \(a_{32}=+1.025006017\) \(a_{33}=+0.516058733\) \(a_{34}=+0.682943244\) \(a_{35}=-0.004911703\)
\(a_{36}=-1.310811680\) \(a_{37}=-0.310603406\) \(a_{38}=+0.269707528\) \(a_{39}=+0.245589655\) \(a_{40}=-0.107055871\)
\(a_{41}=+1.439774528\) \(a_{42}=+0.044345313\) \(a_{43}=+0.738910723\) \(a_{44}=+0.198358649\) \(a_{45}=+0.219224037\)
\(a_{46}=-0.856965743\) \(a_{47}=+0.661371752\) \(a_{48}=-0.177580501\) \(a_{49}=-0.998038721\) \(a_{50}=-0.573245091\)
\(a_{51}=-2.030166348\) \(a_{52}=+0.094397845\) \(a_{53}=+1.436619693\) \(a_{54}=-0.977932497\) \(a_{55}=-0.033174089\)
\(a_{56}=+0.042748188\) \(a_{57}=-0.801752053\) \(a_{58}=-0.150344575\) \(a_{59}=+1.057099027\) \(a_{60}=+0.126893545\)
\(a_{61}=-0.500214925\) \(a_{62}=-0.476352659\) \(a_{63}=-0.087537752\) \(a_{64}=+0.491969426\) \(a_{65}=-0.015787376\)
\(a_{66}=+0.299512304\) \(a_{67}=-1.745106522\) \(a_{68}=-0.780339578\) \(a_{69}=+2.547478182\) \(a_{70}=-0.002850674\)
\(a_{71}=-0.840051814\) \(a_{72}=-1.907979970\) \(a_{73}=+0.266026710\) \(a_{74}=-0.180269290\) \(a_{75}=+1.704069705\)
\(a_{76}=-0.308171229\) \(a_{77}=+0.013246655\) \(a_{78}=+0.142536341\) \(a_{79}=+0.925877637\) \(a_{80}=+0.011415506\)
\(a_{81}=+0.930441030\) \(a_{82}=+0.835622301\) \(a_{83}=+0.807030554\) \(a_{84}=-0.050669515\) \(a_{85}=+0.130506307\)
\(a_{86}=+0.428852064\) \(a_{87}=+0.446925127\) \(a_{88}=+0.288725173\) \(a_{89}=-0.105999788\) \(a_{90}=+0.127234154\)
\(a_{91}=+0.006304014\) \(a_{92}=+0.979179884\) \(a_{93}=+1.416040273\) \(a_{94}=+0.383849676\) \(a_{95}=+0.051539471\)
\(a_{96}=-1.768434433\) \(a_{97}=+0.436451730\) \(a_{98}=-0.579245845\) \(a_{99}=-0.591237986\) \(a_{100}=+0.654997082\)

Showing 100 of 546 available coefficients

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