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: \( 1.36941174922 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+1.452037424\) \(a_{4}=+0.500000000\) \(a_{5}=-1.203127221\)
\(a_{6}=-1.026745509\) \(a_{7}=-0.439149628\) \(a_{8}=-0.353553390\) \(a_{9}=+1.108412680\) \(a_{10}=+0.850739417\)
\(a_{11}=+0.301511345\) \(a_{12}=+0.726018710\) \(a_{13}=+0.206109000\) \(a_{14}=+0.310525681\) \(a_{15}=-1.746985750\)
\(a_{16}=+0.250000001\) \(a_{17}=+0.459171770\) \(a_{18}=-0.783766126\) \(a_{19}=+0.139027155\) \(a_{20}=-0.601563609\)
\(a_{21}=-0.637661682\) \(a_{22}=-0.213200713\) \(a_{23}=+1.472706402\) \(a_{24}=-0.513372758\) \(a_{25}=+0.447515083\)
\(a_{26}=-0.145741077\) \(a_{27}=+0.157419321\) \(a_{28}=-0.219574781\) \(a_{29}=-1.106050788\) \(a_{30}=+1.235305407\)
\(a_{31}=-0.455861646\) \(a_{32}=-0.176776708\) \(a_{33}=+0.437805713\) \(a_{34}=-0.324683458\) \(a_{35}=+0.528352849\)
\(a_{36}=+0.554206320\) \(a_{37}=+0.988013530\) \(a_{38}=-0.098306984\) \(a_{39}=+0.299277993\) \(a_{40}=+0.425369613\)
\(a_{41}=-1.635368320\) \(a_{42}=+0.450894855\) \(a_{43}=+1.346963438\) \(a_{44}=+0.150755732\) \(a_{45}=-1.333561398\)
\(a_{46}=-1.041360682\) \(a_{47}=-1.592917613\) \(a_{48}=+0.363009384\) \(a_{49}=-0.807147672\) \(a_{50}=-0.316440969\)
\(a_{51}=+0.666734628\) \(a_{52}=+0.103054516\) \(a_{53}=+0.889002933\) \(a_{54}=-0.111312190\) \(a_{55}=-0.362756550\)
\(a_{56}=+0.155262845\) \(a_{57}=+0.201872625\) \(a_{58}=+0.782095964\) \(a_{59}=+0.413603864\) \(a_{60}=-0.873492960\)
\(a_{61}=+0.182468801\) \(a_{62}=+0.322342909\) \(a_{63}=-0.486759022\) \(a_{64}=+0.125000043\) \(a_{65}=-0.247975372\)
\(a_{66}=-0.309575434\) \(a_{67}=-0.263858256\) \(a_{68}=+0.229585857\) \(a_{69}=+2.138424864\) \(a_{70}=-0.373601907\)
\(a_{71}=+1.521974321\) \(a_{72}=-0.391883072\) \(a_{73}=+0.484435394\) \(a_{74}=-0.698630962\) \(a_{75}=+0.649808606\)
\(a_{76}=+0.069513618\) \(a_{77}=-0.132408527\) \(a_{78}=-0.211621514\) \(a_{79}=-0.922784108\) \(a_{80}=-0.300781844\)
\(a_{81}=-0.879833972\) \(a_{82}=+1.156379875\) \(a_{83}=-0.597504612\) \(a_{84}=-0.318830714\) \(a_{85}=-0.552442171\)
\(a_{86}=-0.952447037\) \(a_{87}=-1.606027020\) \(a_{88}=-0.106600438\) \(a_{89}=-0.450602424\) \(a_{90}=+0.942970411\)
\(a_{91}=-0.090512750\) \(a_{92}=+0.736353239\) \(a_{93}=-0.661928231\) \(a_{94}=+1.126362821\) \(a_{95}=-0.167267378\)
\(a_{96}=-0.256686351\) \(a_{97}=+0.181936578\) \(a_{98}=+0.570739481\) \(a_{99}=+0.334199045\) \(a_{100}=+0.223757508\)

Showing 100 of 1500 available coefficients

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