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: \( 3.67969872473 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.098089160\) \(a_{3}=-0.751972758\) \(a_{4}=-1.347132782\) \(a_{5}=+0.972674327\)
\(a_{6}=-0.825733112\) \(a_{7}=-1.447597467\) \(a_{8}=-0.672227601\) \(a_{9}=-0.434536974\) \(a_{10}=+1.068083132\)
\(a_{11}=-0.301511345\) \(a_{12}=+1.013007147\) \(a_{13}=+0.531041655\) \(a_{14}=-1.589591086\) \(a_{15}=-0.731424593\)
\(a_{16}=+1.559640342\) \(a_{17}=-0.748483380\) \(a_{18}=-0.477160339\) \(a_{19}=-0.355909058\) \(a_{20}=-1.310321471\)
\(a_{21}=+1.088553860\) \(a_{22}=-0.331086340\) \(a_{23}=-0.758558656\) \(a_{24}=+0.505496840\) \(a_{25}=-0.053904656\)
\(a_{26}=+0.583131101\) \(a_{27}=+1.078732710\) \(a_{28}=+1.950106001\) \(a_{29}=+1.183046027\) \(a_{30}=-0.803169452\)
\(a_{31}=-1.877592686\) \(a_{32}=+0.179187281\) \(a_{33}=+0.226728303\) \(a_{34}=-0.821901471\) \(a_{35}=-1.408040939\)
\(a_{36}=+0.585378998\) \(a_{37}=-0.065792133\) \(a_{38}=-0.390819868\) \(a_{39}=-0.399328832\) \(a_{40}=-0.653858631\)
\(a_{41}=-0.376072145\) \(a_{42}=+1.195329202\) \(a_{43}=+1.613528361\) \(a_{44}=+0.406175809\) \(a_{45}=-0.422662999\)
\(a_{46}=-0.832964990\) \(a_{47}=-0.256350972\) \(a_{48}=-1.172807046\) \(a_{49}=+1.095538465\) \(a_{50}=-0.059192219\)
\(a_{51}=+0.562839159\) \(a_{52}=-0.715383622\) \(a_{53}=+0.259372704\) \(a_{54}=+1.184544780\) \(a_{55}=-0.293272368\)
\(a_{56}=+0.973115185\) \(a_{57}=+0.267633793\) \(a_{58}=+1.299089985\) \(a_{59}=-1.396625575\) \(a_{60}=+0.985325870\)
\(a_{61}=-0.513058467\) \(a_{62}=-2.061764156\) \(a_{63}=+0.629034490\) \(a_{64}=-1.616285784\) \(a_{65}=+0.516530641\)
\(a_{66}=+0.248967996\) \(a_{67}=+0.062975227\) \(a_{68}=+1.008306543\) \(a_{69}=+0.570415512\) \(a_{70}=-1.546154359\)
\(a_{71}=-1.410403035\) \(a_{72}=+0.292107719\) \(a_{73}=+0.979505424\) \(a_{74}=-0.072245695\) \(a_{75}=+0.040534855\)
\(a_{76}=+0.479456764\) \(a_{77}=+0.436467016\) \(a_{78}=-0.438498702\) \(a_{79}=-1.392512732\) \(a_{80}=+1.517022162\)
\(a_{81}=-0.376640711\) \(a_{82}=-0.412960734\) \(a_{83}=+0.894494076\) \(a_{84}=-1.466426572\) \(a_{85}=-0.728030569\)
\(a_{86}=+1.771798027\) \(a_{87}=-0.889618406\) \(a_{88}=+0.202684283\) \(a_{89}=+0.104940998\) \(a_{90}=-0.464121618\)
\(a_{91}=-0.768734617\) \(a_{92}=+1.021879241\) \(a_{93}=+1.411898594\) \(a_{94}=-0.281496220\) \(a_{95}=-0.346183638\)
\(a_{96}=-0.134743901\) \(a_{97}=-0.064369374\) \(a_{98}=+1.202998865\) \(a_{99}=+0.131017829\) \(a_{100}=+0.072616677\)

Showing 100 of 1500 available coefficients

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