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: \( 4.5010075965 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.453528493\) \(a_{3}=+1.176505954\) \(a_{4}=-0.794311906\) \(a_{5}=-1.622638106\)
\(a_{6}=+0.533578972\) \(a_{7}=-0.043840131\) \(a_{8}=-0.813771575\) \(a_{9}=+0.384166259\) \(a_{10}=-0.735912615\)
\(a_{11}=-1.446931043\) \(a_{12}=-0.934512686\) \(a_{13}=+1.733829597\) \(a_{14}=-0.019882749\) \(a_{15}=-1.909043392\)
\(a_{16}=+0.425243309\) \(a_{17}=-1.288329075\) \(a_{18}=+0.174230345\) \(a_{19}=+0.483610933\) \(a_{20}=+1.288880766\)
\(a_{21}=-0.051578175\) \(a_{22}=-0.656224456\) \(a_{23}=+0.208514414\) \(a_{24}=-0.957407103\) \(a_{25}=+1.632954423\)
\(a_{26}=+0.786341125\) \(a_{27}=-0.724532063\) \(a_{28}=+0.034822738\) \(a_{29}=-0.503784939\) \(a_{30}=-0.865805573\)
\(a_{31}=-0.249440935\) \(a_{32}=+1.006631533\) \(a_{33}=-1.702322987\) \(a_{34}=-0.584293944\) \(a_{35}=+0.071136667\)
\(a_{36}=-0.305147833\) \(a_{37}=-0.972417685\) \(a_{38}=+0.219331338\) \(a_{39}=+2.039860843\) \(a_{40}=+1.320456767\)
\(a_{41}=+0.145692433\) \(a_{42}=-0.023392172\) \(a_{43}=-0.067916524\) \(a_{44}=+1.149314555\) \(a_{45}=-0.623362811\)
\(a_{46}=+0.094567228\) \(a_{47}=-0.092517077\) \(a_{48}=+0.500301285\) \(a_{49}=-0.998078043\) \(a_{50}=+0.740591359\)
\(a_{51}=-1.515726827\) \(a_{52}=-1.377201491\) \(a_{53}=-0.346095528\) \(a_{54}=-0.328595935\) \(a_{55}=+2.347845448\)
\(a_{56}=+0.035675853\) \(a_{57}=+0.568971142\) \(a_{58}=-0.228480824\) \(a_{59}=-0.561420384\) \(a_{60}=+1.516375895\)
\(a_{61}=-1.181505593\) \(a_{62}=-0.113128571\) \(a_{63}=-0.016841899\) \(a_{64}=+0.031292773\) \(a_{65}=-2.813377973\)
\(a_{66}=-0.772051979\) \(a_{67}=+1.327828284\) \(a_{68}=+1.023335123\) \(a_{69}=+0.245318450\) \(a_{70}=+0.032262506\)
\(a_{71}=-0.695435796\) \(a_{72}=-0.312623582\) \(a_{73}=+0.753564508\) \(a_{74}=-0.441019128\) \(a_{75}=+1.921180601\)
\(a_{76}=-0.384137922\) \(a_{77}=+0.063433647\) \(a_{78}=+0.925135015\) \(a_{79}=+0.138408828\) \(a_{80}=-0.690015998\)
\(a_{81}=-1.236582544\) \(a_{82}=+0.066075669\) \(a_{83}=+0.079457811\) \(a_{84}=+0.040969159\) \(a_{85}=+2.090491850\)
\(a_{86}=-0.030802079\) \(a_{87}=-0.592705980\) \(a_{88}=+1.177471354\) \(a_{89}=-0.363551288\) \(a_{90}=-0.282712796\)
\(a_{91}=-0.076011317\) \(a_{92}=-0.165625482\) \(a_{93}=-0.293468745\) \(a_{94}=-0.041959131\) \(a_{95}=-0.784725528\)
\(a_{96}=+1.184307991\) \(a_{97}=-0.076935219\) \(a_{98}=-0.452656831\) \(a_{99}=-0.555862086\) \(a_{100}=-1.297075140\)

Showing 100 of 546 available coefficients

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