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: \( 5.03928639222 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-0.473567555\) \(a_{4}=+0.500000000\) \(a_{5}=+0.997811404\)
\(a_{6}=+0.334862830\) \(a_{7}=+0.110562607\) \(a_{8}=-0.353553391\) \(a_{9}=-0.775733771\) \(a_{10}=-0.705559210\)
\(a_{11}=-0.301511345\) \(a_{12}=-0.236783778\) \(a_{13}=+0.401648094\) \(a_{14}=-0.078179569\) \(a_{15}=-0.472531107\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.493081013\) \(a_{18}=+0.548526610\) \(a_{19}=-1.709298899\) \(a_{20}=+0.498905702\)
\(a_{21}=-0.052358864\) \(a_{22}=+0.213200716\) \(a_{23}=-1.108861508\) \(a_{24}=+0.167431415\) \(a_{25}=-0.004372402\)
\(a_{26}=-0.284008091\) \(a_{27}=+0.840929901\) \(a_{28}=+0.055281304\) \(a_{29}=-0.813906345\) \(a_{30}=+0.334129950\)
\(a_{31}=+0.176581585\) \(a_{32}=-0.176776695\) \(a_{33}=+0.142785990\) \(a_{34}=+0.348660928\) \(a_{35}=+0.110320630\)
\(a_{36}=-0.387866885\) \(a_{37}=+0.162298255\) \(a_{38}=+1.208656842\) \(a_{39}=-0.190207506\) \(a_{40}=-0.352779605\)
\(a_{41}=+0.458067474\) \(a_{42}=+0.037023307\) \(a_{43}=-0.527300328\) \(a_{44}=-0.150755672\) \(a_{45}=-0.774036003\)
\(a_{46}=+0.784083492\) \(a_{47}=-1.857752628\) \(a_{48}=-0.118391889\) \(a_{49}=-0.987775910\) \(a_{50}=+0.003091755\)
\(a_{51}=+0.233507170\) \(a_{52}=+0.200824047\) \(a_{53}=+1.463934500\) \(a_{54}=-0.594627235\) \(a_{55}=-0.300851458\)
\(a_{56}=-0.039089785\) \(a_{57}=+0.809468501\) \(a_{58}=+0.575518696\) \(a_{59}=+1.548714334\) \(a_{60}=-0.236265554\)
\(a_{61}=+0.039948561\) \(a_{62}=-0.124862036\) \(a_{63}=-0.085767148\) \(a_{64}=+0.125000000\) \(a_{65}=+0.400769048\)
\(a_{66}=-0.100964942\) \(a_{67}=-0.806914008\) \(a_{68}=-0.246540507\) \(a_{69}=+0.525120834\) \(a_{70}=-0.078008466\)
\(a_{71}=+0.316744038\) \(a_{72}=+0.274263305\) \(a_{73}=-1.462508144\) \(a_{74}=-0.114762196\) \(a_{75}=+0.002070628\)
\(a_{76}=-0.854649449\) \(a_{77}=-0.033335880\) \(a_{78}=+0.134497017\) \(a_{79}=-0.782113356\) \(a_{80}=+0.249452851\)
\(a_{81}=+0.377496653\) \(a_{82}=-0.323902617\) \(a_{83}=-0.789991784\) \(a_{84}=-0.026179432\) \(a_{85}=-0.492001858\)
\(a_{86}=+0.372857637\) \(a_{87}=+0.385439638\) \(a_{88}=+0.106600358\) \(a_{89}=+1.840231571\) \(a_{90}=+0.547326106\)
\(a_{91}=+0.044407260\) \(a_{92}=-0.554430754\) \(a_{93}=-0.083623309\) \(a_{94}=+1.313629481\) \(a_{95}=-1.705557934\)
\(a_{96}=+0.083715707\) \(a_{97}=+0.872969906\) \(a_{98}=+0.698463044\) \(a_{99}=+0.233892532\) \(a_{100}=-0.002186201\)

Showing 100 of 238 available coefficients

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