Properties

Level $21$
Weight $0$
Character 21.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 21 = 3 \cdot 7 \)
Weight: \( 0 \)
Character: 21.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 6.4217178814 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.934991788\) \(a_{3}=-0.577350269\) \(a_{4}=+2.744193219\) \(a_{5}=-0.615505989\)
\(a_{6}=+1.117168030\) \(a_{7}=-0.377964473\) \(a_{8}=-3.374999555\) \(a_{9}=+0.333333333\) \(a_{10}=+1.190999033\)
\(a_{11}=-1.397758785\) \(a_{12}=-1.584360694\) \(a_{13}=-1.079478420\) \(a_{14}=+0.731358151\) \(a_{15}=+0.355362548\)
\(a_{16}=+3.786403204\) \(a_{17}=-0.839149300\) \(a_{18}=-0.644997263\) \(a_{19}=-0.083910412\) \(a_{20}=-1.689067360\)
\(a_{21}=+0.218217890\) \(a_{22}=+2.704651770\) \(a_{23}=-1.068887903\) \(a_{24}=+1.948556901\) \(a_{25}=-0.621152378\)
\(a_{26}=+2.088781878\) \(a_{27}=-0.192450090\) \(a_{28}=-1.037207544\) \(a_{29}=+0.476929050\) \(a_{30}=-0.687623613\)
\(a_{31}=-0.247572752\) \(a_{32}=-3.951659549\) \(a_{33}=+0.806996411\) \(a_{34}=+1.623747004\) \(a_{35}=+0.232639397\)
\(a_{36}=+0.914731073\) \(a_{37}=+0.737846643\) \(a_{38}=+0.162365958\) \(a_{39}=+0.623237156\) \(a_{40}=+2.077332438\)
\(a_{41}=+0.392057324\) \(a_{42}=-0.422249826\) \(a_{43}=+0.063975139\) \(a_{44}=-3.835720179\) \(a_{45}=-0.205168663\)
\(a_{46}=+2.068289314\) \(a_{47}=+0.650449531\) \(a_{48}=-2.186080909\) \(a_{49}=+0.142857143\) \(a_{50}=+1.201924750\)
\(a_{51}=+0.484483074\) \(a_{52}=-2.962297360\) \(a_{53}=-1.425306152\) \(a_{54}=+0.372389343\) \(a_{55}=+0.860328903\)
\(a_{56}=+1.275629928\) \(a_{57}=+0.048445699\) \(a_{58}=-0.922853794\) \(a_{59}=-0.702316910\) \(a_{60}=+0.975183495\)
\(a_{61}=+0.688404420\) \(a_{62}=+0.479051242\) \(a_{63}=-0.125988158\) \(a_{64}=+3.860025573\) \(a_{65}=+0.664425432\)
\(a_{66}=-1.561531428\) \(a_{67}=+0.002481036\) \(a_{68}=-2.302787818\) \(a_{69}=+0.617122719\) \(a_{70}=-0.450155322\)
\(a_{71}=+1.502650151\) \(a_{72}=-1.124999852\) \(a_{73}=+1.286772482\) \(a_{74}=-1.427727195\) \(a_{75}=+0.358622493\)
\(a_{76}=-0.230266384\) \(a_{77}=+0.528303163\) \(a_{78}=-1.205958779\) \(a_{79}=-1.728069503\) \(a_{80}=-2.330553847\)
\(a_{81}=+0.111111111\) \(a_{82}=-0.758627702\) \(a_{83}=+1.168065761\) \(a_{84}=+0.598832055\) \(a_{85}=+0.516501419\)
\(a_{86}=-0.123791369\) \(a_{87}=-0.275355115\) \(a_{88}=+4.717435277\) \(a_{89}=+1.088522470\) \(a_{90}=+0.396999678\)
\(a_{91}=+0.408004492\) \(a_{92}=-2.933234935\) \(a_{93}=+0.142936195\) \(a_{94}=-1.258614501\) \(a_{95}=+0.051647361\)
\(a_{96}=+2.281491705\) \(a_{97}=-1.859539580\) \(a_{98}=-0.276427398\) \(a_{99}=-0.465919595\) \(a_{100}=-1.704562143\)

Showing 100 of 226 available coefficients

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