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: \( 7.01263487678 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+0.754463155\) \(a_{4}=+0.500000000\) \(a_{5}=+1.463784281\)
\(a_{6}=+0.533486013\) \(a_{7}=+0.945191011\) \(a_{8}=+0.353553391\) \(a_{9}=-0.430785347\) \(a_{10}=+1.035051792\)
\(a_{11}=+0.301511345\) \(a_{12}=+0.377231578\) \(a_{13}=-0.725956089\) \(a_{14}=+0.668350973\) \(a_{15}=+1.104371308\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.681976464\) \(a_{18}=-0.304611240\) \(a_{19}=+1.658015155\) \(a_{20}=+0.731892141\)
\(a_{21}=+0.713111793\) \(a_{22}=+0.213200716\) \(a_{23}=+1.707081126\) \(a_{24}=+0.266743007\) \(a_{25}=+1.142664423\)
\(a_{26}=-0.513328474\) \(a_{27}=-1.079474828\) \(a_{28}=+0.472595505\) \(a_{29}=-0.253908045\) \(a_{30}=+0.780908441\)
\(a_{31}=-0.438780554\) \(a_{32}=+0.176776695\) \(a_{33}=+0.227479200\) \(a_{34}=-1.189336963\) \(a_{35}=+1.383555745\)
\(a_{36}=-0.215392674\) \(a_{37}=+0.385608196\) \(a_{38}=+1.172393759\) \(a_{39}=-0.547707122\) \(a_{40}=+0.517525896\)
\(a_{41}=-0.468435070\) \(a_{42}=+0.504246184\) \(a_{43}=+0.324471569\) \(a_{44}=+0.150755672\) \(a_{45}=-0.630576820\)
\(a_{46}=+1.207088640\) \(a_{47}=-1.378415915\) \(a_{48}=+0.188615789\) \(a_{49}=-0.106613953\) \(a_{50}=+0.807985762\)
\(a_{51}=-1.268989270\) \(a_{52}=-0.362978045\) \(a_{53}=+0.717908958\) \(a_{54}=-0.763303971\) \(a_{55}=+0.441347567\)
\(a_{56}=+0.334175487\) \(a_{57}=+1.250911345\) \(a_{58}=-0.179540101\) \(a_{59}=-0.401514125\) \(a_{60}=+0.552185654\)
\(a_{61}=-1.524093541\) \(a_{62}=-0.310264705\) \(a_{63}=-0.407174438\) \(a_{64}=+0.125000000\) \(a_{65}=-1.062643113\)
\(a_{66}=+0.160852085\) \(a_{67}=+0.685557249\) \(a_{68}=-0.840988232\) \(a_{69}=+1.287929813\) \(a_{70}=+0.978321649\)
\(a_{71}=+0.424102560\) \(a_{72}=-0.152305620\) \(a_{73}=-0.632409843\) \(a_{74}=+0.272666170\) \(a_{75}=+0.862098206\)
\(a_{76}=+0.829007577\) \(a_{77}=+0.284985813\) \(a_{78}=-0.387287420\) \(a_{79}=+0.692337168\) \(a_{80}=+0.365946070\)
\(a_{81}=-0.383638637\) \(a_{82}=-0.331233614\) \(a_{83}=-0.834326082\) \(a_{84}=+0.356555896\) \(a_{85}=-2.462050709\)
\(a_{86}=+0.229436047\) \(a_{87}=-0.191564265\) \(a_{88}=+0.106600358\) \(a_{89}=-0.257707668\) \(a_{90}=-0.445885145\)
\(a_{91}=-0.686167171\) \(a_{92}=+0.853540563\) \(a_{93}=-0.331043761\) \(a_{94}=-0.974687241\) \(a_{95}=+2.426976522\)
\(a_{96}=+0.133371503\) \(a_{97}=-0.050584329\) \(a_{98}=-0.075387449\) \(a_{99}=-0.129886669\) \(a_{100}=+0.571332211\)

Showing 100 of 268 available coefficients

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