Properties

Level $22$
Weight $0$
Character 22.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 22 = 2 \cdot 11 \)
Weight: \( 0 \)
Character: 22.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 2.27226262876 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-0.843037850\) \(a_{4}=+0.500000000\) \(a_{5}=+1.882117673\)
\(a_{6}=-0.596117781\) \(a_{7}=-0.768204903\) \(a_{8}=+0.353553391\) \(a_{9}=-0.289287183\) \(a_{10}=+1.330858170\)
\(a_{11}=+0.301511345\) \(a_{12}=-0.421518925\) \(a_{13}=-0.083300984\) \(a_{14}=-0.543202896\) \(a_{15}=-1.586696437\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.489448112\) \(a_{18}=-0.204556929\) \(a_{19}=-0.586332365\) \(a_{20}=+0.941058837\)
\(a_{21}=+0.647625810\) \(a_{22}=+0.213200716\) \(a_{23}=-0.662635215\) \(a_{24}=-0.298058890\) \(a_{25}=+2.542366936\)
\(a_{26}=-0.058902690\) \(a_{27}=+1.086917895\) \(a_{28}=-0.384102451\) \(a_{29}=-1.142266971\) \(a_{30}=-1.121963810\)
\(a_{31}=-0.637276034\) \(a_{32}=+0.176776696\) \(a_{33}=-0.254185476\) \(a_{34}=+0.346092079\) \(a_{35}=-1.445852024\)
\(a_{36}=-0.144643591\) \(a_{37}=+0.959089852\) \(a_{38}=-0.414599592\) \(a_{39}=+0.070225881\) \(a_{40}=+0.665429084\)
\(a_{41}=-0.470115276\) \(a_{42}=+0.457940605\) \(a_{43}=+0.432255646\) \(a_{44}=+0.150755668\) \(a_{45}=-0.544472526\)
\(a_{46}=-0.468553852\) \(a_{47}=+0.504135209\) \(a_{48}=-0.210759454\) \(a_{49}=-0.409861238\) \(a_{50}=+1.797724878\)
\(a_{51}=-0.412623288\) \(a_{52}=-0.041650459\) \(a_{53}=+0.915972159\) \(a_{54}=+0.768566995\) \(a_{55}=+0.567479762\)
\(a_{56}=-0.271601484\) \(a_{57}=+0.494300450\) \(a_{58}=-0.807704716\) \(a_{59}=-0.437532162\) \(a_{60}=-0.793348224\)
\(a_{61}=-1.747547514\) \(a_{62}=-0.450622242\) \(a_{63}=+0.222231730\) \(a_{64}=+0.124999994\) \(a_{65}=-0.156782106\)
\(a_{66}=-0.179736250\) \(a_{67}=+0.832424474\) \(a_{68}=+0.244724126\) \(a_{69}=+0.558626258\) \(a_{70}=-1.022370711\)
\(a_{71}=+1.427316439\) \(a_{72}=-0.102279152\) \(a_{73}=-0.476200343\) \(a_{74}=+0.678179885\) \(a_{75}=-2.143302687\)
\(a_{76}=-0.293165768\) \(a_{77}=-0.231622288\) \(a_{78}=+0.049645186\) \(a_{79}=+1.325054459\) \(a_{80}=+0.470546911\)
\(a_{81}=-0.627056256\) \(a_{82}=-0.332441177\) \(a_{83}=-0.700308108\) \(a_{84}=+0.323795571\) \(a_{85}=+0.920907617\)
\(a_{86}=+0.305650939\) \(a_{87}=+0.962974432\) \(a_{88}=+0.106600892\) \(a_{89}=+0.535773749\) \(a_{90}=-0.385000507\)
\(a_{91}=+0.063991992\) \(a_{92}=-0.331318393\) \(a_{93}=+0.537242793\) \(a_{94}=+0.356478268\) \(a_{95}=-1.103553670\)
\(a_{96}=-0.149029731\) \(a_{97}=+0.929799027\) \(a_{98}=-0.289812598\) \(a_{99}=-0.087211681\) \(a_{100}=+1.271176091\)

Showing 100 of 1500 available coefficients

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