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: \( 7.60956467074 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-1.891669568\) \(a_{4}=+0.500000000\) \(a_{5}=-1.288066001\)
\(a_{6}=+1.337612379\) \(a_{7}=-1.008728072\) \(a_{8}=-0.353553391\) \(a_{9}=+2.578413753\) \(a_{10}=+0.910800204\)
\(a_{11}=+0.301511345\) \(a_{12}=-0.945834784\) \(a_{13}=+0.974269354\) \(a_{14}=+0.713278460\) \(a_{15}=+2.436595255\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.983649980\) \(a_{18}=-1.823213849\) \(a_{19}=-1.091477662\) \(a_{20}=-0.644033000\)
\(a_{21}=+1.908180196\) \(a_{22}=-0.213200716\) \(a_{23}=-0.836951865\) \(a_{24}=+0.668806189\) \(a_{25}=+0.659114022\)
\(a_{26}=-0.688912467\) \(a_{27}=-2.985837261\) \(a_{28}=-0.504364036\) \(a_{29}=+0.298077523\) \(a_{30}=-1.722933028\)
\(a_{31}=+1.224356479\) \(a_{32}=-0.176776695\) \(a_{33}=-0.570359835\) \(a_{34}=-0.695545571\) \(a_{35}=+1.299308334\)
\(a_{36}=+1.289206876\) \(a_{37}=-0.689388401\) \(a_{38}=+0.771791256\) \(a_{39}=-1.842995688\) \(a_{40}=+0.455400102\)
\(a_{41}=+0.934854792\) \(a_{42}=-1.349287157\) \(a_{43}=+0.732311045\) \(a_{44}=+0.150755672\) \(a_{45}=-3.321167091\)
\(a_{46}=+0.591814339\) \(a_{47}=+0.438641063\) \(a_{48}=-0.472917392\) \(a_{49}=+0.017532324\) \(a_{50}=-0.466063995\)
\(a_{51}=-1.860740732\) \(a_{52}=+0.487134677\) \(a_{53}=+0.137135582\) \(a_{54}=+2.111305775\) \(a_{55}=-0.388366512\)
\(a_{56}=+0.356639230\) \(a_{57}=+2.064715077\) \(a_{58}=-0.210772637\) \(a_{59}=+1.185179583\) \(a_{60}=+1.218297627\)
\(a_{61}=-0.612635939\) \(a_{62}=-0.865750769\) \(a_{63}=-2.600918334\) \(a_{64}=+0.125000000\) \(a_{65}=-1.254923231\)
\(a_{66}=+0.403305307\) \(a_{67}=-0.423307111\) \(a_{68}=+0.491824990\) \(a_{69}=+1.583236372\) \(a_{70}=-0.918749734\)
\(a_{71}=+0.923919732\) \(a_{72}=-0.911606925\) \(a_{73}=+0.140561232\) \(a_{74}=+0.487471213\) \(a_{75}=-1.246825938\)
\(a_{76}=-0.545738831\) \(a_{77}=-0.304142957\) \(a_{78}=+1.303194748\) \(a_{79}=-0.875077271\) \(a_{80}=-0.322016500\)
\(a_{81}=+3.069803727\) \(a_{82}=-0.661042163\) \(a_{83}=-1.566482490\) \(a_{84}=+0.954090098\) \(a_{85}=-1.267006095\)
\(a_{86}=-0.517822106\) \(a_{87}=-0.563864178\) \(a_{88}=-0.106600358\) \(a_{89}=+1.739650033\) \(a_{90}=+2.348419771\)
\(a_{91}=-0.982772847\) \(a_{92}=-0.418475932\) \(a_{93}=-2.316077891\) \(a_{94}=-0.310166070\) \(a_{95}=+1.405895267\)
\(a_{96}=+0.334403095\) \(a_{97}=+0.705065968\) \(a_{98}=-0.012397225\) \(a_{99}=+0.777420997\) \(a_{100}=+0.329557011\)

Showing 100 of 262 available coefficients

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