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: \( 6.7113188158 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+1.293528250\) \(a_{4}=+0.500000000\) \(a_{5}=-0.863065782\)
\(a_{6}=-0.914662598\) \(a_{7}=+0.055412355\) \(a_{8}=-0.353553391\) \(a_{9}=+0.673215335\) \(a_{10}=+0.610279667\)
\(a_{11}=-0.301511345\) \(a_{12}=+0.646764125\) \(a_{13}=+0.119760127\) \(a_{14}=-0.039182452\) \(a_{15}=-1.116399971\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.187323608\) \(a_{18}=-0.476035128\) \(a_{19}=-1.661941403\) \(a_{20}=-0.431532891\)
\(a_{21}=+0.071677446\) \(a_{22}=+0.213200716\) \(a_{23}=+0.801911734\) \(a_{24}=-0.457331299\) \(a_{25}=-0.255117456\)
\(a_{26}=-0.084683198\) \(a_{27}=-0.422705196\) \(a_{28}=+0.027706177\) \(a_{29}=-1.669760510\) \(a_{30}=+0.789413990\)
\(a_{31}=-1.268482185\) \(a_{32}=-0.176776695\) \(a_{33}=-0.390013442\) \(a_{34}=-0.132457793\) \(a_{35}=-0.047824507\)
\(a_{36}=+0.336607667\) \(a_{37}=-0.458650148\) \(a_{38}=+1.175170036\) \(a_{39}=+0.154913108\) \(a_{40}=+0.305139833\)
\(a_{41}=+1.016404972\) \(a_{42}=-0.050683608\) \(a_{43}=-0.574034641\) \(a_{44}=-0.150755672\) \(a_{45}=-0.581029119\)
\(a_{46}=-0.567037225\) \(a_{47}=+0.687764519\) \(a_{48}=+0.323382063\) \(a_{49}=-0.996929471\) \(a_{50}=+0.180395283\)
\(a_{51}=+0.242308379\) \(a_{52}=+0.059880064\) \(a_{53}=-0.312950461\) \(a_{54}=+0.298897711\) \(a_{55}=+0.260224124\)
\(a_{56}=-0.019591226\) \(a_{57}=-2.149768155\) \(a_{58}=+1.180698979\) \(a_{59}=-0.219909895\) \(a_{60}=-0.558199985\)
\(a_{61}=-1.590520812\) \(a_{62}=+0.896952355\) \(a_{63}=+0.037304447\) \(a_{64}=+0.125000000\) \(a_{65}=-0.103360868\)
\(a_{66}=+0.275781150\) \(a_{67}=+1.959591760\) \(a_{68}=+0.093661804\) \(a_{69}=+1.037295482\) \(a_{70}=+0.033817033\)
\(a_{71}=+0.571320827\) \(a_{72}=-0.238017564\) \(a_{73}=-0.127382105\) \(a_{74}=+0.324314630\) \(a_{75}=-0.330001637\)
\(a_{76}=-0.830970701\) \(a_{77}=-0.016707454\) \(a_{78}=-0.109540109\) \(a_{79}=+1.209504094\) \(a_{80}=-0.215766445\)
\(a_{81}=-1.219996448\) \(a_{82}=-0.718706848\) \(a_{83}=-0.937437026\) \(a_{84}=+0.035838723\) \(a_{85}=-0.161672596\)
\(a_{86}=+0.405903787\) \(a_{87}=-2.159882391\) \(a_{88}=+0.106600358\) \(a_{89}=+1.892789263\) \(a_{90}=+0.410849630\)
\(a_{91}=+0.006636191\) \(a_{92}=+0.400955867\) \(a_{93}=-1.640817541\) \(a_{94}=-0.486322955\) \(a_{95}=+1.434364756\)
\(a_{96}=-0.228665649\) \(a_{97}=+0.812606692\) \(a_{98}=+0.704935589\) \(a_{99}=-0.202982061\) \(a_{100}=-0.127558728\)

Showing 100 of 250 available coefficients

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