Properties

Level $23$
Weight $0$
Character 23.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 23 \)
Weight: \( 0 \)
Character: 23.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 2.46433387048 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.186771621\) \(a_{3}=+1.811173589\) \(a_{4}=-0.965116362\) \(a_{5}=-0.389220925\)
\(a_{6}=+0.338275827\) \(a_{7}=+0.911076008\) \(a_{8}=-0.367027968\) \(a_{9}=+2.280349770\) \(a_{10}=-0.072695423\)
\(a_{11}=-0.520775631\) \(a_{12}=-1.747993265\) \(a_{13}=-0.348293539\) \(a_{14}=+0.170163143\) \(a_{15}=-0.704946660\)
\(a_{16}=+0.896565953\) \(a_{17}=+0.575138554\) \(a_{18}=+0.425904623\) \(a_{19}=-1.856701465\) \(a_{20}=+0.375643483\)
\(a_{21}=+1.650116804\) \(a_{22}=-0.097266109\) \(a_{23}=-0.208514414\) \(a_{24}=-0.664751362\) \(a_{25}=-0.848507071\)
\(a_{26}=-0.065051349\) \(a_{27}=+2.318935689\) \(a_{28}=-0.879294362\) \(a_{29}=+0.898691207\) \(a_{30}=-0.131664030\)
\(a_{31}=+1.157155024\) \(a_{32}=+0.534481044\) \(a_{33}=-0.943215069\) \(a_{34}=+0.107419560\) \(a_{35}=-0.354609847\)
\(a_{36}=-2.200802874\) \(a_{37}=-0.864543633\) \(a_{38}=-0.346779142\) \(a_{39}=-0.630820060\) \(a_{40}=+0.142854965\)
\(a_{41}=+1.062805406\) \(a_{42}=+0.308194990\) \(a_{43}=-0.316002732\) \(a_{44}=+0.502609082\) \(a_{45}=-0.887559847\)
\(a_{46}=-0.038944575\) \(a_{47}=+0.901216696\) \(a_{48}=+1.623836575\) \(a_{49}=-0.169940507\) \(a_{50}=-0.158477041\)
\(a_{51}=+1.041675759\) \(a_{52}=+0.336143793\) \(a_{53}=+0.044463237\) \(a_{54}=+0.433111377\) \(a_{55}=+0.202696773\)
\(a_{56}=-0.334390376\) \(a_{57}=-3.362808656\) \(a_{58}=+0.167850013\) \(a_{59}=-0.259366379\) \(a_{60}=+0.680355556\)
\(a_{61}=+0.394514148\) \(a_{62}=+0.216123719\) \(a_{63}=+2.077571966\) \(a_{64}=-0.796740062\) \(a_{65}=+0.135563134\)
\(a_{66}=-0.176165807\) \(a_{67}=-0.057157346\) \(a_{68}=-0.555075629\) \(a_{69}=-0.377655800\) \(a_{70}=-0.066231056\)
\(a_{71}=+0.017310875\) \(a_{72}=-0.836952143\) \(a_{73}=-0.001503702\) \(a_{74}=-0.161472216\) \(a_{75}=-1.536793598\)
\(a_{76}=+1.791932962\) \(a_{77}=-0.474466183\) \(a_{78}=-0.117819285\) \(a_{79}=-0.087560859\) \(a_{80}=-0.348962230\)
\(a_{81}=+1.919645305\) \(a_{82}=+0.198501888\) \(a_{83}=-1.364714419\) \(a_{84}=-1.592554726\) \(a_{85}=-0.223855960\)
\(a_{86}=-0.059020342\) \(a_{87}=+1.627685779\) \(a_{88}=+0.191139222\) \(a_{89}=+0.469716689\) \(a_{90}=-0.165770991\)
\(a_{91}=-0.317321887\) \(a_{92}=+0.201240673\) \(a_{93}=+2.095808618\) \(a_{94}=+0.168321703\) \(a_{95}=+0.722667062\)
\(a_{96}=+0.968037952\) \(a_{97}=-1.358633483\) \(a_{98}=-0.031740064\) \(a_{99}=-1.187550591\) \(a_{100}=+0.818908058\)

Showing 100 of 546 available coefficients

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