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: \( 4.44254652128 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-0.400588543\) \(a_{4}=+0.500000000\) \(a_{5}=+0.780704859\)
\(a_{6}=-0.283258876\) \(a_{7}=+1.609090476\) \(a_{8}=+0.353553386\) \(a_{9}=-0.839528818\) \(a_{10}=+0.552041698\)
\(a_{11}=+0.301511344\) \(a_{12}=-0.200294271\) \(a_{13}=+1.826722769\) \(a_{14}=+1.137798787\) \(a_{15}=-0.312741422\)
\(a_{16}=+0.250000001\) \(a_{17}=-0.864365212\) \(a_{18}=-0.593636522\) \(a_{19}=+0.336101988\) \(a_{20}=+0.390352428\)
\(a_{21}=-0.644583210\) \(a_{22}=+0.213200720\) \(a_{23}=-1.265471332\) \(a_{24}=-0.141629438\) \(a_{25}=-0.390499925\)
\(a_{26}=+1.291688055\) \(a_{27}=+0.736894172\) \(a_{28}=+0.804545240\) \(a_{29}=+0.711790323\) \(a_{30}=-0.221141580\)
\(a_{31}=-0.442165217\) \(a_{32}=+0.176776695\) \(a_{33}=-0.120781989\) \(a_{34}=-0.611198506\) \(a_{35}=+1.256224751\)
\(a_{36}=-0.419764406\) \(a_{37}=-1.065553275\) \(a_{38}=+0.237659997\) \(a_{39}=-0.731764208\) \(a_{40}=+0.276020840\)
\(a_{41}=+0.855272674\) \(a_{42}=-0.455789144\) \(a_{43}=-0.504699863\) \(a_{44}=+0.150755676\) \(a_{45}=-0.655424234\)
\(a_{46}=-0.894823400\) \(a_{47}=-0.381927285\) \(a_{48}=-0.100147107\) \(a_{49}=+1.589172135\) \(a_{50}=-0.276125135\)
\(a_{51}=+0.346254786\) \(a_{52}=+0.913361370\) \(a_{53}=-0.397411056\) \(a_{54}=+0.521062820\) \(a_{55}=+0.235391394\)
\(a_{56}=+0.568899437\) \(a_{57}=-0.134638612\) \(a_{58}=+0.503311776\) \(a_{59}=-1.636324000\) \(a_{60}=-0.156370803\)
\(a_{61}=+1.273758482\) \(a_{62}=-0.312658012\) \(a_{63}=-1.350877771\) \(a_{64}=+0.124999986\) \(a_{65}=+1.426131448\)
\(a_{66}=-0.085405793\) \(a_{67}=-0.156535534\) \(a_{68}=-0.432182633\) \(a_{69}=+0.506933371\) \(a_{70}=+0.888285048\)
\(a_{71}=-0.752115755\) \(a_{72}=-0.296818259\) \(a_{73}=-0.643002558\) \(a_{74}=-0.753459927\) \(a_{75}=+0.156429741\)
\(a_{76}=+0.168051035\) \(a_{77}=+0.485159002\) \(a_{78}=-0.517435380\) \(a_{79}=-1.197730616\) \(a_{80}=+0.195176212\)
\(a_{81}=+0.544337402\) \(a_{82}=+0.604769093\) \(a_{83}=+0.332276963\) \(a_{84}=-0.322291546\) \(a_{85}=-0.674814100\)
\(a_{86}=-0.356876778\) \(a_{87}=-0.285135085\) \(a_{88}=+0.106600355\) \(a_{89}=-0.805505537\) \(a_{90}=-0.463454929\)
\(a_{91}=+2.939362217\) \(a_{92}=-0.632735592\) \(a_{93}=+0.177126380\) \(a_{94}=-0.270063385\) \(a_{95}=+0.262396423\)
\(a_{96}=-0.070814727\) \(a_{97}=+1.682666111\) \(a_{98}=+1.123714372\) \(a_{99}=-0.253127475\) \(a_{100}=-0.195249937\)

Showing 100 of 1500 available coefficients

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