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: \( 5.07378943223 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+0.182719874\) \(a_{4}=+0.500000000\) \(a_{5}=-0.181740086\)
\(a_{6}=-0.129202462\) \(a_{7}=+1.082929230\) \(a_{8}=-0.353553391\) \(a_{9}=-0.966613448\) \(a_{10}=+0.128509647\)
\(a_{11}=+0.301511345\) \(a_{12}=+0.091359937\) \(a_{13}=-1.869063639\) \(a_{14}=-0.765746602\) \(a_{15}=-0.033207526\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.489616567\) \(a_{18}=+0.683498924\) \(a_{19}=-0.715501522\) \(a_{20}=-0.090870043\)
\(a_{21}=+0.197872693\) \(a_{22}=-0.213200716\) \(a_{23}=+0.513544819\) \(a_{24}=-0.064601231\) \(a_{25}=-0.966970541\)
\(a_{26}=+1.321627573\) \(a_{27}=-0.359339362\) \(a_{28}=+0.541464615\) \(a_{29}=-0.741919129\) \(a_{30}=+0.023481267\)
\(a_{31}=-0.349945810\) \(a_{32}=-0.176776695\) \(a_{33}=+0.055092115\) \(a_{34}=+0.346211195\) \(a_{35}=-0.196811651\)
\(a_{36}=-0.483306724\) \(a_{37}=-1.232946838\) \(a_{38}=+0.505935978\) \(a_{39}=-0.341515073\) \(a_{40}=+0.064254824\)
\(a_{41}=+0.052452743\) \(a_{42}=-0.139917123\) \(a_{43}=+1.715849672\) \(a_{44}=+0.150755672\) \(a_{45}=+0.175672411\)
\(a_{46}=-0.363131024\) \(a_{47}=+0.807755260\) \(a_{48}=+0.045679969\) \(a_{49}=+0.172735717\) \(a_{50}=+0.683751427\)
\(a_{51}=-0.089462678\) \(a_{52}=-0.934531819\) \(a_{53}=-0.450726452\) \(a_{54}=+0.254091299\) \(a_{55}=-0.054796698\)
\(a_{56}=-0.382873301\) \(a_{57}=-0.130736348\) \(a_{58}=+0.524616048\) \(a_{59}=-0.807587724\) \(a_{60}=-0.016603763\)
\(a_{61}=-0.360999915\) \(a_{62}=+0.247449055\) \(a_{63}=-1.046773957\) \(a_{64}=+0.125000000\) \(a_{65}=+0.339683786\)
\(a_{66}=-0.038956008\) \(a_{67}=-1.586339741\) \(a_{68}=-0.244808284\) \(a_{69}=+0.093834845\) \(a_{70}=+0.139166853\)
\(a_{71}=+1.088438664\) \(a_{72}=+0.341749462\) \(a_{73}=+1.438425031\) \(a_{74}=+0.871825070\) \(a_{75}=-0.176684736\)
\(a_{76}=-0.357750761\) \(a_{77}=+0.326515448\) \(a_{78}=+0.241487624\) \(a_{79}=-0.863256176\) \(a_{80}=-0.045435021\)
\(a_{81}=+0.900955005\) \(a_{82}=-0.037089691\) \(a_{83}=+0.751997342\) \(a_{84}=+0.098936346\) \(a_{85}=+0.088982957\)
\(a_{86}=-1.213288938\) \(a_{87}=-0.135563370\) \(a_{88}=-0.106600358\) \(a_{89}=+1.131684876\) \(a_{90}=-0.124219153\)
\(a_{91}=-2.024063647\) \(a_{92}=+0.256772410\) \(a_{93}=-0.063942054\) \(a_{94}=-0.571169222\) \(a_{95}=+0.130035308\)
\(a_{96}=-0.032300616\) \(a_{97}=-0.768891910\) \(a_{98}=-0.122142597\) \(a_{99}=-0.291444920\) \(a_{100}=-0.483485271\)

Showing 100 of 282 available coefficients

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