Properties

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

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 22 = 2 \cdot 11 \)
Weight: \( 0 \)
Character: 22.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 2.61952660281 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+0.975604985\) \(a_{4}=+0.500000000\) \(a_{5}=-1.470103768\)
\(a_{6}=+0.689856901\) \(a_{7}=+1.571109261\) \(a_{8}=+0.353553391\) \(a_{9}=-0.048194913\) \(a_{10}=-1.039520343\)
\(a_{11}=+0.301511345\) \(a_{12}=+0.487802492\) \(a_{13}=-0.612234158\) \(a_{14}=+1.110942013\) \(a_{15}=-1.434240564\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.914848271\) \(a_{18}=-0.034078950\) \(a_{19}=+0.099348789\) \(a_{20}=-0.735051884\)
\(a_{21}=+1.532782027\) \(a_{22}=+0.213200716\) \(a_{23}=+0.102658770\) \(a_{24}=+0.344928450\) \(a_{25}=+1.161205088\)
\(a_{26}=-0.432914925\) \(a_{27}=-1.022624183\) \(a_{28}=+0.785554631\) \(a_{29}=+0.371524708\) \(a_{30}=-1.014161229\)
\(a_{31}=+0.996805602\) \(a_{32}=+0.176776695\) \(a_{33}=+0.294155969\) \(a_{34}=-0.646895416\) \(a_{35}=-2.309693643\)
\(a_{36}=-0.024097458\) \(a_{37}=+0.320409234\) \(a_{38}=+0.070250202\) \(a_{39}=-0.597298701\) \(a_{40}=-0.519760169\)
\(a_{41}=-1.120645441\) \(a_{42}=+1.083840567\) \(a_{43}=+0.631708568\) \(a_{44}=+0.150755657\) \(a_{45}=+0.070851530\)
\(a_{46}=+0.072590724\) \(a_{47}=+1.948160672\) \(a_{48}=+0.243901275\) \(a_{49}=+1.468384318\) \(a_{50}=+0.821095937\)
\(a_{51}=-0.892530495\) \(a_{52}=-0.306117081\) \(a_{53}=-1.679246665\) \(a_{54}=-0.723104489\) \(a_{55}=-0.443252962\)
\(a_{56}=+0.555471006\) \(a_{57}=+0.096925162\) \(a_{58}=+0.262707639\) \(a_{59}=+0.052315146\) \(a_{60}=-0.717120294\)
\(a_{61}=-0.152264744\) \(a_{62}=+0.704847991\) \(a_{63}=-0.075719431\) \(a_{64}=+0.125000000\) \(a_{65}=+0.900047734\)
\(a_{66}=+0.207999728\) \(a_{67}=+0.022105590\) \(a_{68}=-0.457424117\) \(a_{69}=+0.100154449\) \(a_{70}=-1.633200058\)
\(a_{71}=-0.388964489\) \(a_{72}=-0.017039490\) \(a_{73}=-1.252351365\) \(a_{74}=+0.226563559\) \(a_{75}=+1.132877314\)
\(a_{76}=+0.049674342\) \(a_{77}=+0.473707421\) \(a_{78}=-0.422354010\) \(a_{79}=+1.158430845\) \(a_{80}=-0.367525975\)
\(a_{81}=-0.949482399\) \(a_{82}=-0.792415914\) \(a_{83}=-1.045350880\) \(a_{84}=+0.766390993\) \(a_{85}=+1.344921877\)
\(a_{86}=+0.446685289\) \(a_{87}=+0.362461333\) \(a_{88}=+0.106600323\) \(a_{89}=+0.473678933\) \(a_{90}=+0.050099604\)
\(a_{91}=-0.961886736\) \(a_{92}=+0.051329395\) \(a_{93}=+0.972488512\) \(a_{94}=+1.377557684\) \(a_{95}=-0.146053017\)
\(a_{96}=+0.172464219\) \(a_{97}=-0.704387010\) \(a_{98}=+1.038304461\) \(a_{99}=-0.014531294\) \(a_{100}=+0.580602558\)

Showing 100 of 1500 available coefficients

Rows: Cols: