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: \( 6.56005701381 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-1.122845934\) \(a_{4}=+0.500000000\) \(a_{5}=+0.417446083\)
\(a_{6}=-0.793971974\) \(a_{7}=-1.265361703\) \(a_{8}=+0.353553391\) \(a_{9}=+0.260782991\) \(a_{10}=+0.295178956\)
\(a_{11}=+0.301511345\) \(a_{12}=-0.561422967\) \(a_{13}=+1.050583643\) \(a_{14}=-0.894745841\) \(a_{15}=-0.468727637\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.844619795\) \(a_{18}=+0.184401421\) \(a_{19}=+0.935923922\) \(a_{20}=+0.208723042\)
\(a_{21}=+1.420806242\) \(a_{22}=+0.213200716\) \(a_{23}=+0.136688895\) \(a_{24}=-0.396985987\) \(a_{25}=-0.825738767\)
\(a_{26}=+0.742874818\) \(a_{27}=+0.830026813\) \(a_{28}=-0.632680851\) \(a_{29}=+1.043451819\) \(a_{30}=-0.331440491\)
\(a_{31}=-0.805968530\) \(a_{32}=+0.176776695\) \(a_{33}=-0.338550787\) \(a_{34}=+1.304343166\) \(a_{35}=-0.528220287\)
\(a_{36}=+0.130391495\) \(a_{37}=+0.450812459\) \(a_{38}=+0.661798152\) \(a_{39}=-1.179643572\) \(a_{40}=+0.147589478\)
\(a_{41}=+0.737312852\) \(a_{42}=+1.004661729\) \(a_{43}=-0.029653049\) \(a_{44}=+0.150755672\) \(a_{45}=+0.108862838\)
\(a_{46}=+0.096653645\) \(a_{47}=-0.844406717\) \(a_{48}=-0.280711483\) \(a_{49}=+0.601140238\) \(a_{50}=-0.583885482\)
\(a_{51}=-2.071223836\) \(a_{52}=+0.525291822\) \(a_{53}=+0.287552997\) \(a_{54}=+0.586917588\) \(a_{55}=+0.125864730\)
\(a_{56}=-0.447372920\) \(a_{57}=-1.050898370\) \(a_{58}=+0.737831857\) \(a_{59}=+1.064521268\) \(a_{60}=-0.234363819\)
\(a_{61}=+0.813339784\) \(a_{62}=-0.569905813\) \(a_{63}=-0.329984809\) \(a_{64}=+0.125000000\) \(a_{65}=+0.438562027\)
\(a_{66}=-0.239391557\) \(a_{67}=-1.282611171\) \(a_{68}=+0.922309898\) \(a_{69}=-0.153480570\) \(a_{70}=-0.373508147\)
\(a_{71}=+1.626047595\) \(a_{72}=+0.092200711\) \(a_{73}=-0.174678478\) \(a_{74}=+0.318772547\) \(a_{75}=+0.927177417\)
\(a_{76}=+0.467961961\) \(a_{77}=-0.381520908\) \(a_{78}=-0.834133969\) \(a_{79}=-1.414950912\) \(a_{80}=+0.104361521\)
\(a_{81}=-1.192775223\) \(a_{82}=+0.521358918\) \(a_{83}=+0.974041920\) \(a_{84}=+0.710403121\) \(a_{85}=+0.770029309\)
\(a_{86}=-0.020967872\) \(a_{87}=-1.171635632\) \(a_{88}=+0.106600358\) \(a_{89}=-0.874325942\) \(a_{90}=+0.076977651\)
\(a_{91}=-1.329368307\) \(a_{92}=+0.068344448\) \(a_{93}=+0.904978486\) \(a_{94}=-0.597085716\) \(a_{95}=+0.390697776\)
\(a_{96}=-0.198492993\) \(a_{97}=-1.770713265\) \(a_{98}=+0.425070339\) \(a_{99}=+0.078629030\) \(a_{100}=-0.412869384\)

Showing 100 of 222 available coefficients

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