Properties

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

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Maass form invariants

Level: \( 18 = 2 \cdot 3^{2} \)
Weight: \( 0 \)
Character: 18.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 9.46886989067 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+0.000000000\) \(a_{4}=+0.500000000\) \(a_{5}=+0.285043562\)
\(a_{6}=+0.000000000\) \(a_{7}=-0.162139289\) \(a_{8}=-0.353553391\) \(a_{9}=+0.000000000\) \(a_{10}=-0.201556236\)
\(a_{11}=-0.309776512\) \(a_{12}=+0.000000000\) \(a_{13}=-1.013516525\) \(a_{14}=+0.114649791\) \(a_{15}=+0.000000000\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.742076554\) \(a_{18}=+0.000000000\) \(a_{19}=+1.341321791\) \(a_{20}=+0.142521781\)
\(a_{21}=+0.000000000\) \(a_{22}=+0.219045072\) \(a_{23}=-0.421794355\) \(a_{24}=+0.000000000\) \(a_{25}=-0.918750168\)
\(a_{26}=+0.716664408\) \(a_{27}=+0.000000000\) \(a_{28}=-0.081069645\) \(a_{29}=+0.711249477\) \(a_{30}=+0.000000000\)
\(a_{31}=-1.254037569\) \(a_{32}=-0.176776695\) \(a_{33}=+0.000000000\) \(a_{34}=-1.231834144\) \(a_{35}=-0.046216761\)
\(a_{36}=+0.000000000\) \(a_{37}=-1.653455686\) \(a_{38}=-0.948457734\) \(a_{39}=+0.000000000\) \(a_{40}=-0.100778118\)
\(a_{41}=+0.317580797\) \(a_{42}=+0.000000000\) \(a_{43}=-0.864967876\) \(a_{44}=-0.154888256\) \(a_{45}=+0.000000000\)
\(a_{46}=+0.298253649\) \(a_{47}=+1.122012900\) \(a_{48}=+0.000000000\) \(a_{49}=-0.973710851\) \(a_{50}=+0.649654474\)
\(a_{51}=+0.000000000\) \(a_{52}=-0.506758263\) \(a_{53}=-0.887021324\) \(a_{54}=+0.000000000\) \(a_{55}=-0.088299800\)
\(a_{56}=+0.057324895\) \(a_{57}=+0.000000000\) \(a_{58}=-0.502929329\) \(a_{59}=-1.727671858\) \(a_{60}=+0.000000000\)
\(a_{61}=+0.694372351\) \(a_{62}=+0.886738469\) \(a_{63}=+0.000000000\) \(a_{64}=+0.125000000\) \(a_{65}=-0.288896360\)
\(a_{66}=+0.000000000\) \(a_{67}=-0.013269105\) \(a_{68}=+0.871038277\) \(a_{69}=+0.000000000\) \(a_{70}=+0.032680185\)
\(a_{71}=-0.358777270\) \(a_{72}=+0.000000000\) \(a_{73}=-1.579703013\) \(a_{74}=+1.169169728\) \(a_{75}=+0.000000000\)
\(a_{76}=+0.670660895\) \(a_{77}=+0.050226944\) \(a_{78}=+0.000000000\) \(a_{79}=+0.383856418\) \(a_{80}=+0.071260890\)
\(a_{81}=+0.000000000\) \(a_{82}=-0.224563535\) \(a_{83}=-1.096136445\) \(a_{84}=+0.000000000\) \(a_{85}=+0.496567706\)
\(a_{86}=+0.611624651\) \(a_{87}=+0.000000000\) \(a_{88}=+0.109522536\) \(a_{89}=-1.834931718\) \(a_{90}=+0.000000000\)
\(a_{91}=+0.164330849\) \(a_{92}=-0.210897178\) \(a_{93}=+0.000000000\) \(a_{94}=-0.793382930\) \(a_{95}=+0.382335141\)
\(a_{96}=+0.000000000\) \(a_{97}=+0.333894278\) \(a_{98}=+0.688517546\) \(a_{99}=+0.000000000\) \(a_{100}=-0.459375084\)

Showing 100 of 250 available coefficients

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