Properties

Level $18$
Weight $0$
Character 18.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 18 = 2 \cdot 3^{2} \)
Weight: \( 0 \)
Character: 18.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 1.9678447101 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+0.000000000\) \(a_{4}=+0.500000000\) \(a_{5}=+0.963742431\)
\(a_{6}=+0.000000000\) \(a_{7}=+0.173726717\) \(a_{8}=-0.353553391\) \(a_{9}=+0.000000000\) \(a_{10}=-0.681468809\)
\(a_{11}=-0.907981993\) \(a_{12}=+0.000000000\) \(a_{13}=+0.767376197\) \(a_{14}=-0.122843340\) \(a_{15}=+0.000000000\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.332992325\) \(a_{18}=+0.000000000\) \(a_{19}=-1.142249765\) \(a_{20}=+0.481871216\)
\(a_{21}=+0.000000000\) \(a_{22}=+0.642040224\) \(a_{23}=-0.521674124\) \(a_{24}=+0.000000000\) \(a_{25}=-0.071200526\)
\(a_{26}=-0.542616913\) \(a_{27}=+0.000000000\) \(a_{28}=+0.086863358\) \(a_{29}=-0.771007741\) \(a_{30}=+0.000000000\)
\(a_{31}=+0.736488529\) \(a_{32}=-0.176776695\) \(a_{33}=+0.000000000\) \(a_{34}=-0.942567913\) \(a_{35}=+0.167427809\)
\(a_{36}=+0.000000000\) \(a_{37}=-0.307633953\) \(a_{38}=+0.807692554\) \(a_{39}=+0.000000000\) \(a_{40}=-0.340734404\)
\(a_{41}=+1.522540923\) \(a_{42}=+0.000000000\) \(a_{43}=+1.316169510\) \(a_{44}=-0.453990996\) \(a_{45}=+0.000000000\)
\(a_{46}=+0.368879311\) \(a_{47}=-0.451215014\) \(a_{48}=+0.000000000\) \(a_{49}=-0.969819028\) \(a_{50}=+0.050346375\)
\(a_{51}=+0.000000000\) \(a_{52}=+0.383688099\) \(a_{53}=-1.324003092\) \(a_{54}=+0.000000000\) \(a_{55}=-0.875060774\)
\(a_{56}=-0.061421670\) \(a_{57}=+0.000000000\) \(a_{58}=+0.545184802\) \(a_{59}=-0.235118700\) \(a_{60}=+0.000000000\)
\(a_{61}=-0.292850430\) \(a_{62}=-0.520776033\) \(a_{63}=+0.000000000\) \(a_{64}=+0.125000000\) \(a_{65}=+0.739553002\)
\(a_{66}=+0.000000000\) \(a_{67}=+0.400303800\) \(a_{68}=+0.666496163\) \(a_{69}=+0.000000000\) \(a_{70}=-0.118389339\)
\(a_{71}=+1.214117139\) \(a_{72}=+0.000000000\) \(a_{73}=+1.145326400\) \(a_{74}=+0.217530054\) \(a_{75}=+0.000000000\)
\(a_{76}=-0.571124882\) \(a_{77}=-0.157740731\) \(a_{78}=+0.000000000\) \(a_{79}=-1.122611100\) \(a_{80}=+0.240935608\)
\(a_{81}=+0.000000000\) \(a_{82}=-1.076599011\) \(a_{83}=-0.946017100\) \(a_{84}=+0.000000000\) \(a_{85}=+1.284661265\)
\(a_{86}=-0.930672386\) \(a_{87}=+0.000000000\) \(a_{88}=+0.321020112\) \(a_{89}=+0.132926000\) \(a_{90}=+0.000000000\)
\(a_{91}=+0.133313747\) \(a_{92}=-0.260837062\) \(a_{93}=+0.000000000\) \(a_{94}=+0.319057196\) \(a_{95}=-1.100834566\)
\(a_{96}=+0.000000000\) \(a_{97}=+0.031346000\) \(a_{98}=+0.685765611\) \(a_{99}=+0.000000000\) \(a_{100}=-0.035600263\)

Showing 100 of 156 available coefficients

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