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: \( 4.34721319308 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-1.366508592\) \(a_{4}=+0.500000000\) \(a_{5}=-1.313199344\)
\(a_{6}=+0.966267492\) \(a_{7}=-0.105126177\) \(a_{8}=-0.353553381\) \(a_{9}=+0.867345737\) \(a_{10}=+0.928572160\)
\(a_{11}=-0.301511339\) \(a_{12}=-0.683254294\) \(a_{13}=+1.449720327\) \(a_{14}=+0.074335431\) \(a_{15}=+1.794498189\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.560228560\) \(a_{18}=-0.613306052\) \(a_{19}=-0.743641648\) \(a_{20}=-0.656599672\)
\(a_{21}=+0.143655818\) \(a_{22}=+0.213200711\) \(a_{23}=+1.423686518\) \(a_{24}=+0.483133747\) \(a_{25}=+0.724492526\)
\(a_{26}=-1.025107067\) \(a_{27}=+0.181273198\) \(a_{28}=-0.052563099\) \(a_{29}=+0.597043838\) \(a_{30}=-1.268901843\)
\(a_{31}=-0.373353725\) \(a_{32}=-0.176776681\) \(a_{33}=+0.412017870\) \(a_{34}=+1.103248187\) \(a_{35}=+0.138051569\)
\(a_{36}=+0.433672861\) \(a_{37}=+0.761125433\) \(a_{38}=+0.525834079\) \(a_{39}=-1.981055272\) \(a_{40}=+0.464286080\)
\(a_{41}=-1.411208473\) \(a_{42}=-0.101580043\) \(a_{43}=+1.140032539\) \(a_{44}=-0.150755631\) \(a_{45}=-1.138997891\)
\(a_{46}=-1.006698413\) \(a_{47}=+0.921696138\) \(a_{48}=-0.341627145\) \(a_{49}=-0.988948540\) \(a_{50}=-0.512293544\)
\(a_{51}=+2.132065768\) \(a_{52}=+0.724860063\) \(a_{53}=-1.200668073\) \(a_{54}=-0.128179437\) \(a_{55}=+0.395944471\)
\(a_{56}=+0.037167691\) \(a_{57}=+1.016192737\) \(a_{58}=-0.422173808\) \(a_{59}=+0.882931696\) \(a_{60}=+0.897249173\)
\(a_{61}=+1.600608705\) \(a_{62}=+0.264000925\) \(a_{63}=-0.091180796\) \(a_{64}=+0.125000067\) \(a_{65}=-1.903771848\)
\(a_{66}=-0.291340669\) \(a_{67}=+0.457239302\) \(a_{68}=-0.780114354\) \(a_{69}=-1.945479861\) \(a_{70}=-0.097617188\)
\(a_{71}=+0.148654187\) \(a_{72}=-0.306653045\) \(a_{73}=+0.615985548\) \(a_{74}=-0.538196929\) \(a_{75}=-0.990025230\)
\(a_{76}=-0.371820875\) \(a_{77}=+0.031696717\) \(a_{78}=+1.400817652\) \(a_{79}=+0.930453132\) \(a_{80}=-0.328299761\)
\(a_{81}=-1.115057064\) \(a_{82}=+0.997875044\) \(a_{83}=-0.392978939\) \(a_{84}=+0.071827806\) \(a_{85}=+2.048891207\)
\(a_{86}=-0.806124764\) \(a_{87}=-0.815865519\) \(a_{88}=+0.106600431\) \(a_{89}=-0.838701880\) \(a_{90}=+0.805393121\)
\(a_{91}=-0.152403602\) \(a_{92}=+0.711843236\) \(a_{93}=+0.510191128\) \(a_{94}=-0.651737557\) \(a_{95}=+0.976549824\)
\(a_{96}=+0.241566819\) \(a_{97}=-0.805333599\) \(a_{98}=+0.699292214\) \(a_{99}=-0.261514616\) \(a_{100}=+0.362246264\)

Showing 100 of 1500 available coefficients

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