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: \( 6.05930133683 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+0.849819727\) \(a_{4}=+0.500000000\) \(a_{5}=+1.865379848\)
\(a_{6}=+0.600913292\) \(a_{7}=-0.568416679\) \(a_{8}=+0.353553391\) \(a_{9}=-0.277806431\) \(a_{10}=+1.319022740\)
\(a_{11}=-0.301511345\) \(a_{12}=+0.424909864\) \(a_{13}=+1.402368403\) \(a_{14}=-0.401931288\) \(a_{15}=+1.585236593\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.632963234\) \(a_{18}=-0.196438811\) \(a_{19}=-0.910443624\) \(a_{20}=+0.932689924\)
\(a_{21}=-0.483051707\) \(a_{22}=-0.213200716\) \(a_{23}=+0.050046357\) \(a_{24}=+0.300456646\) \(a_{25}=+2.479641977\)
\(a_{26}=+0.991624208\) \(a_{27}=-1.085905113\) \(a_{28}=-0.284208339\) \(a_{29}=+0.705823365\) \(a_{30}=+1.120931545\)
\(a_{31}=-1.338644633\) \(a_{32}=+0.176776695\) \(a_{33}=-0.256230289\) \(a_{34}=+0.447572595\) \(a_{35}=-1.060313017\)
\(a_{36}=-0.138903216\) \(a_{37}=-1.153935927\) \(a_{38}=-0.643780860\) \(a_{39}=+1.191760334\) \(a_{40}=+0.659511370\)
\(a_{41}=+0.836338902\) \(a_{42}=-0.341569137\) \(a_{43}=+0.016996129\) \(a_{44}=-0.150755672\) \(a_{45}=-0.518214519\)
\(a_{46}=+0.035388119\) \(a_{47}=+0.537528042\) \(a_{48}=+0.212454932\) \(a_{49}=-0.676902480\) \(a_{50}=+1.753371657\)
\(a_{51}=+0.537904642\) \(a_{52}=+0.701184202\) \(a_{53}=-1.230772160\) \(a_{54}=-0.767850869\) \(a_{55}=-0.562433186\)
\(a_{56}=-0.200965644\) \(a_{57}=-0.773712952\) \(a_{58}=+0.499092488\) \(a_{59}=+0.812574333\) \(a_{60}=+0.792618297\)
\(a_{61}=-0.571827050\) \(a_{62}=-0.946564698\) \(a_{63}=+0.157909809\) \(a_{64}=+0.125000000\) \(a_{65}=+2.615949758\)
\(a_{66}=-0.181182175\) \(a_{67}=-1.435144306\) \(a_{68}=+0.316481617\) \(a_{69}=+0.042530382\) \(a_{70}=-0.749754525\)
\(a_{71}=-1.811661701\) \(a_{72}=-0.098219406\) \(a_{73}=-1.424836023\) \(a_{74}=-0.815955919\) \(a_{75}=+2.107248668\)
\(a_{76}=-0.455221812\) \(a_{77}=+0.171384077\) \(a_{78}=+0.842701814\) \(a_{79}=+0.202642455\) \(a_{80}=+0.466344962\)
\(a_{81}=-0.645017155\) \(a_{82}=+0.591380909\) \(a_{83}=+1.601518773\) \(a_{84}=-0.241525853\) \(a_{85}=+1.180716860\)
\(a_{86}=+0.012018078\) \(a_{87}=+0.599822620\) \(a_{88}=-0.106600358\) \(a_{89}=+0.354935907\) \(a_{90}=-0.366433000\)
\(a_{91}=-0.797129590\) \(a_{92}=+0.025023179\) \(a_{93}=-1.137606617\) \(a_{94}=+0.380089723\) \(a_{95}=-1.698323188\)
\(a_{96}=+0.150228323\) \(a_{97}=-0.179320319\) \(a_{98}=-0.478642334\) \(a_{99}=+0.083761791\) \(a_{100}=+1.239820988\)

Showing 100 of 250 available coefficients

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