Properties

Level $22$
Weight $0$
Character 22.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 22 = 2 \cdot 11 \)
Weight: \( 0 \)
Character: 22.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 3.03564960868 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+1.045421092\) \(a_{4}=+0.500000000\) \(a_{5}=+1.626013255\)
\(a_{6}=-0.739224343\) \(a_{7}=+0.087632452\) \(a_{8}=-0.353553391\) \(a_{9}=+0.092905260\) \(a_{10}=-1.149764999\)
\(a_{11}=+0.301511345\) \(a_{12}=+0.522710546\) \(a_{13}=+0.866035110\) \(a_{14}=-0.061965501\) \(a_{15}=+1.699868552\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.951509542\) \(a_{18}=-0.065693939\) \(a_{19}=-0.608591473\) \(a_{20}=+0.813006627\)
\(a_{21}=+0.091612814\) \(a_{22}=-0.213200716\) \(a_{23}=-0.055928223\) \(a_{24}=-0.369612172\) \(a_{25}=+1.643919105\)
\(a_{26}=-0.612379299\) \(a_{27}=-0.948295974\) \(a_{28}=+0.043816226\) \(a_{29}=-0.929600103\) \(a_{30}=-1.201988581\)
\(a_{31}=+1.291743884\) \(a_{32}=-0.176776695\) \(a_{33}=+0.315206319\) \(a_{34}=+1.379925631\) \(a_{35}=+0.142491529\)
\(a_{36}=+0.046452630\) \(a_{37}=-0.969908973\) \(a_{38}=+0.430339157\) \(a_{39}=+0.905371370\) \(a_{40}=-0.574882499\)
\(a_{41}=+0.191970377\) \(a_{42}=-0.064780042\) \(a_{43}=+0.456367432\) \(a_{44}=+0.150755672\) \(a_{45}=+0.151065184\)
\(a_{46}=+0.039547226\) \(a_{47}=+0.766962389\) \(a_{48}=+0.261355273\) \(a_{49}=-0.992320553\) \(a_{50}=-1.162426347\)
\(a_{51}=-2.040149237\) \(a_{52}=+0.433017555\) \(a_{53}=-0.738093742\) \(a_{54}=+0.670546514\) \(a_{55}=+0.490261443\)
\(a_{56}=-0.030982751\) \(a_{57}=-0.636234362\) \(a_{58}=+0.657326536\) \(a_{59}=-0.065869286\) \(a_{60}=+0.849934276\)
\(a_{61}=-0.201820301\) \(a_{62}=-0.913400860\) \(a_{63}=+0.008141516\) \(a_{64}=+0.125000000\) \(a_{65}=+1.408184568\)
\(a_{66}=-0.222884526\) \(a_{67}=+1.131062510\) \(a_{68}=-0.975754771\) \(a_{69}=-0.058468544\) \(a_{70}=-0.100756727\)
\(a_{71}=-1.305083734\) \(a_{72}=-0.032846970\) \(a_{73}=+1.535551619\) \(a_{74}=+0.685829212\) \(a_{75}=+1.718587705\)
\(a_{76}=-0.304295736\) \(a_{77}=+0.026422179\) \(a_{78}=-0.640194235\) \(a_{79}=+1.115145172\) \(a_{80}=+0.406503314\)
\(a_{81}=-1.084273872\) \(a_{82}=-0.135743555\) \(a_{83}=+1.127704176\) \(a_{84}=+0.045806407\) \(a_{85}=-3.173180382\)
\(a_{86}=-0.322700506\) \(a_{87}=-0.971823555\) \(a_{88}=-0.106600358\) \(a_{89}=-1.246112046\) \(a_{90}=-0.106819216\)
\(a_{91}=+0.075892781\) \(a_{92}=-0.027964112\) \(a_{93}=+1.350416302\) \(a_{94}=-0.542324306\) \(a_{95}=-0.989577801\)
\(a_{96}=-0.184806086\) \(a_{97}=+1.140166476\) \(a_{98}=+0.701676592\) \(a_{99}=+0.028011990\) \(a_{100}=+0.821959552\)

Showing 100 of 226 available coefficients

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