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: \( 3.83392687084 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+1.630314850\) \(a_{4}=+0.500000000\) \(a_{5}=-0.349114148\)
\(a_{6}=-1.152806686\) \(a_{7}=+1.678807765\) \(a_{8}=-0.353553391\) \(a_{9}=+1.657926509\) \(a_{10}=+0.246860981\)
\(a_{11}=-0.301511345\) \(a_{12}=+0.815157425\) \(a_{13}=+0.370659312\) \(a_{14}=-1.187096355\) \(a_{15}=-0.569165979\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.992301839\) \(a_{18}=-1.172331077\) \(a_{19}=-0.361774150\) \(a_{20}=-0.174557074\)
\(a_{21}=+2.736985229\) \(a_{22}=+0.213200716\) \(a_{23}=-1.743096939\) \(a_{24}=-0.576403343\) \(a_{25}=-0.878119312\)
\(a_{26}=-0.262095713\) \(a_{27}=+1.072627358\) \(a_{28}=+0.839403882\) \(a_{29}=+0.361804054\) \(a_{30}=+0.402461123\)
\(a_{31}=+1.119176973\) \(a_{32}=-0.176776695\) \(a_{33}=-0.491558422\) \(a_{34}=-0.701663360\) \(a_{35}=-0.586095542\)
\(a_{36}=+0.828963255\) \(a_{37}=-0.792150356\) \(a_{38}=+0.255812955\) \(a_{39}=+0.604291380\) \(a_{40}=+0.123430491\)
\(a_{41}=-0.884590351\) \(a_{42}=-1.935340816\) \(a_{43}=+0.160494036\) \(a_{44}=-0.150755672\) \(a_{45}=-0.578805600\)
\(a_{46}=+1.232555666\) \(a_{47}=-1.621203304\) \(a_{48}=+0.407578711\) \(a_{49}=+1.818395511\) \(a_{50}=+0.620924123\)
\(a_{51}=+1.617764426\) \(a_{52}=+0.185329653\) \(a_{53}=-0.297414988\) \(a_{54}=-0.758462079\) \(a_{55}=+0.105261866\)
\(a_{56}=-0.593548168\) \(a_{57}=-0.589805752\) \(a_{58}=-0.255834108\) \(a_{59}=+0.683796652\) \(a_{60}=-0.284582998\)
\(a_{61}=-0.070210298\) \(a_{62}=-0.791377612\) \(a_{63}=+2.783339937\) \(a_{64}=+0.125000064\) \(a_{65}=-0.129402526\)
\(a_{66}=+0.347584294\) \(a_{67}=+0.579766465\) \(a_{68}=+0.496150920\) \(a_{69}=-2.841796824\) \(a_{70}=+0.414432130\)
\(a_{71}=-1.507730337\) \(a_{72}=-0.586165547\) \(a_{73}=+0.791098271\) \(a_{74}=+0.560134888\) \(a_{75}=-1.431610946\)
\(a_{76}=-0.180887093\) \(a_{77}=-0.506179568\) \(a_{78}=-0.427298544\) \(a_{79}=-0.144465623\) \(a_{80}=-0.087278548\)
\(a_{81}=+0.090793796\) \(a_{82}=+0.625499830\) \(a_{83}=-0.119416036\) \(a_{84}=+1.368492695\) \(a_{85}=-0.346426698\)
\(a_{86}=-0.113486422\) \(a_{87}=+0.589854603\) \(a_{88}=+0.106600362\) \(a_{89}=+0.781037052\) \(a_{90}=+0.409277363\)
\(a_{91}=+0.622265730\) \(a_{92}=-0.871548479\) \(a_{93}=+1.824610840\) \(a_{94}=+1.146363837\) \(a_{95}=+0.126300467\)
\(a_{96}=-0.288201686\) \(a_{97}=-0.633850081\) \(a_{98}=-1.285799798\) \(a_{99}=-0.499883566\) \(a_{100}=-0.439059657\)

Showing 100 of 1500 available coefficients

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