Properties

Level $82$
Weight $0$
Character 82.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 82 = 2 \cdot 41 \)
Weight: \( 0 \)
Character: 82.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 1.30603228445 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+0.257378138\) \(a_{4}=+0.500000000\) \(a_{5}=+1.715109091\)
\(a_{6}=-0.181993827\) \(a_{7}=-0.907139744\) \(a_{8}=-0.353553391\) \(a_{9}=-0.933756494\) \(a_{10}=-1.212765269\)
\(a_{11}=-0.692343877\) \(a_{12}=+0.128689069\) \(a_{13}=+1.618052916\) \(a_{14}=+0.641444665\) \(a_{15}=+0.441431585\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.418392246\) \(a_{18}=+0.660265549\) \(a_{19}=-0.200070908\) \(a_{20}=+0.857554545\)
\(a_{21}=-0.233477938\) \(a_{22}=+0.489561050\) \(a_{23}=+0.665057422\) \(a_{24}=-0.090996913\) \(a_{25}=+1.941599193\)
\(a_{26}=-1.144136189\) \(a_{27}=-0.497706646\) \(a_{28}=-0.453569872\) \(a_{29}=-0.711335107\) \(a_{30}=-0.312139267\)
\(a_{31}=+1.312209856\) \(a_{32}=-0.176776695\) \(a_{33}=-0.178194178\) \(a_{34}=+0.295847994\) \(a_{35}=-1.555843622\)
\(a_{36}=-0.466878247\) \(a_{37}=+1.542999980\) \(a_{38}=+0.141471496\) \(a_{39}=+0.416451447\) \(a_{40}=-0.606382634\)
\(a_{41}=-0.156173762\) \(a_{42}=+0.165093834\) \(a_{43}=-0.072516038\) \(a_{44}=-0.346171939\) \(a_{45}=-1.601494251\)
\(a_{46}=-0.470266613\) \(a_{47}=-1.473554886\) \(a_{48}=+0.064344535\) \(a_{49}=-0.177097484\) \(a_{50}=-1.372917956\)
\(a_{51}=-0.107685017\) \(a_{52}=+0.809026458\) \(a_{53}=+1.623730918\) \(a_{54}=+0.351931744\) \(a_{55}=-1.187445278\)
\(a_{56}=+0.320722332\) \(a_{57}=-0.051493878\) \(a_{58}=+0.502989878\) \(a_{59}=+0.656076429\) \(a_{60}=+0.220715792\)
\(a_{61}=-0.350402478\) \(a_{62}=-0.927872487\) \(a_{63}=+0.847047627\) \(a_{64}=+0.125000000\) \(a_{65}=+2.775137265\)
\(a_{66}=+0.126002312\) \(a_{67}=-0.357373472\) \(a_{68}=-0.209196123\) \(a_{69}=+0.171171241\) \(a_{70}=+1.100147576\)
\(a_{71}=-1.651788358\) \(a_{72}=+0.330132774\) \(a_{73}=+0.415094616\) \(a_{74}=-1.091065749\) \(a_{75}=+0.499725185\)
\(a_{76}=-0.100035454\) \(a_{77}=+0.628052648\) \(a_{78}=-0.294475642\) \(a_{79}=+0.134958277\) \(a_{80}=+0.428777273\)
\(a_{81}=+0.805657684\) \(a_{82}=+0.110431526\) \(a_{83}=-1.280683025\) \(a_{84}=-0.116738969\) \(a_{85}=-0.717588345\)
\(a_{86}=+0.051276582\) \(a_{87}=-0.183082105\) \(a_{88}=+0.244780525\) \(a_{89}=+0.282127671\) \(a_{90}=+1.132427445\)
\(a_{91}=-1.467800109\) \(a_{92}=+0.332528711\) \(a_{93}=+0.337734129\) \(a_{94}=+1.041960652\) \(a_{95}=-0.343143434\)
\(a_{96}=-0.045498457\) \(a_{97}=-1.220017339\) \(a_{98}=+0.125226832\) \(a_{99}=+0.646480591\) \(a_{100}=+0.970799597\)

Showing 100 of 672 available coefficients

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