Properties

Level $23$
Weight $0$
Character 23.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 23 \)
Weight: \( 0 \)
Character: 23.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 4.19680364676 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.587659555\) \(a_{3}=-1.376677469\) \(a_{4}=-0.654656248\) \(a_{5}=-0.228527021\)
\(a_{6}=+0.809017668\) \(a_{7}=-0.146036727\) \(a_{8}=+0.972374554\) \(a_{9}=+0.895240854\) \(a_{10}=+0.134296087\)
\(a_{11}=-1.171252460\) \(a_{12}=+0.901250506\) \(a_{13}=-0.519907528\) \(a_{14}=+0.085819878\) \(a_{15}=+0.314608001\)
\(a_{16}=+0.083231051\) \(a_{17}=-0.192923528\) \(a_{18}=-0.526096841\) \(a_{19}=+1.886856203\) \(a_{20}=+0.149606642\)
\(a_{21}=+0.201045472\) \(a_{22}=+0.688297699\) \(a_{23}=+0.208514414\) \(a_{24}=-1.338646139\) \(a_{25}=-0.947775401\)
\(a_{26}=+0.305528626\) \(a_{27}=+0.144219556\) \(a_{28}=+0.095603856\) \(a_{29}=-0.028756756\) \(a_{30}=-0.184882398\)
\(a_{31}=-0.173876721\) \(a_{32}=-1.021286076\) \(a_{33}=+1.612436872\) \(a_{34}=+0.113373354\) \(a_{35}=+0.033373338\)
\(a_{36}=-0.586075018\) \(a_{37}=-0.111710205\) \(a_{38}=-1.108829076\) \(a_{39}=+0.715744979\) \(a_{40}=-0.222213860\)
\(a_{41}=+1.221575623\) \(a_{42}=-0.118146293\) \(a_{43}=-0.676639529\) \(a_{44}=+0.766767741\) \(a_{45}=-0.204586726\)
\(a_{46}=-0.122535488\) \(a_{47}=+1.304724054\) \(a_{48}=-0.114582312\) \(a_{49}=-0.978673274\) \(a_{50}=+0.556969270\)
\(a_{51}=+0.265593474\) \(a_{52}=+0.340360711\) \(a_{53}=+1.514671330\) \(a_{54}=-0.084752000\) \(a_{55}=+0.267662836\)
\(a_{56}=-0.142002397\) \(a_{57}=-2.597592422\) \(a_{58}=+0.016899183\) \(a_{59}=-1.210230218\) \(a_{60}=-0.205960094\)
\(a_{61}=-1.499864845\) \(a_{62}=+0.102180316\) \(a_{63}=-0.130738044\) \(a_{64}=+0.516937470\) \(a_{65}=+0.118812919\)
\(a_{66}=-0.947563934\) \(a_{67}=+1.283783164\) \(a_{68}=+0.126298593\) \(a_{69}=-0.287057096\) \(a_{70}=-0.019612161\)
\(a_{71}=+1.258441202\) \(a_{72}=+0.870509426\) \(a_{73}=+1.255974215\) \(a_{74}=+0.065647569\) \(a_{75}=+1.304781040\)
\(a_{76}=-1.235242202\) \(a_{77}=+0.171045876\) \(a_{78}=-0.420614376\) \(a_{79}=+0.790587821\) \(a_{80}=-0.019020544\)
\(a_{81}=-1.093784667\) \(a_{82}=-0.717870586\) \(a_{83}=+0.274850189\) \(a_{84}=-0.131615674\) \(a_{85}=+0.044088239\)
\(a_{86}=+0.397633684\) \(a_{87}=+0.039588778\) \(a_{88}=-1.138896088\) \(a_{89}=+0.506507775\) \(a_{90}=+0.120227344\)
\(a_{91}=+0.075925594\) \(a_{92}=-0.136505264\) \(a_{93}=+0.239372164\) \(a_{94}=-0.766733557\) \(a_{95}=-0.431197627\)
\(a_{96}=+1.405981530\) \(a_{97}=-1.191191216\) \(a_{98}=+0.575126700\) \(a_{99}=-1.048553052\) \(a_{100}=+0.620467088\)

Showing 100 of 546 available coefficients

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