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: \( 14.8156276656 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+0.000000000\) \(a_{4}=+0.500000000\) \(a_{5}=-1.665860719\)
\(a_{6}=+0.000000000\) \(a_{7}=+0.438147542\) \(a_{8}=-0.353553391\) \(a_{9}=+0.000000000\) \(a_{10}=+1.177941411\)
\(a_{11}=+0.501514949\) \(a_{12}=+0.000000000\) \(a_{13}=+0.186446198\) \(a_{14}=-0.309817098\) \(a_{15}=+0.000000000\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.810041046\) \(a_{18}=+0.000000000\) \(a_{19}=+0.358040547\) \(a_{20}=-0.832930359\)
\(a_{21}=+0.000000000\) \(a_{22}=-0.354624621\) \(a_{23}=-1.217858972\) \(a_{24}=+0.000000000\) \(a_{25}=+1.775091934\)
\(a_{26}=-0.131837371\) \(a_{27}=+0.000000000\) \(a_{28}=+0.219073771\) \(a_{29}=+1.413148840\) \(a_{30}=+0.000000000\)
\(a_{31}=-1.732019712\) \(a_{32}=-0.176776695\) \(a_{33}=+0.000000000\) \(a_{34}=+1.279892298\) \(a_{35}=-0.729892779\)
\(a_{36}=+0.000000000\) \(a_{37}=-0.966259978\) \(a_{38}=-0.253172899\) \(a_{39}=+0.000000000\) \(a_{40}=+0.588970705\)
\(a_{41}=-0.889352268\) \(a_{42}=+0.000000000\) \(a_{43}=+0.832855069\) \(a_{44}=+0.250757475\) \(a_{45}=+0.000000000\)
\(a_{46}=+0.861156337\) \(a_{47}=-0.873580864\) \(a_{48}=+0.000000000\) \(a_{49}=-0.808026731\) \(a_{50}=-1.255179544\)
\(a_{51}=+0.000000000\) \(a_{52}=+0.093223099\) \(a_{53}=-0.313956185\) \(a_{54}=+0.000000000\) \(a_{55}=-0.835454054\)
\(a_{56}=-0.154908549\) \(a_{57}=+0.000000000\) \(a_{58}=-0.999247127\) \(a_{59}=-0.123708516\) \(a_{60}=+0.000000000\)
\(a_{61}=-1.255501923\) \(a_{62}=+1.224722883\) \(a_{63}=+0.000000000\) \(a_{64}=+0.125000000\) \(a_{65}=-0.310593398\)
\(a_{66}=+0.000000000\) \(a_{67}=+0.958649313\) \(a_{68}=-0.905020523\) \(a_{69}=+0.000000000\) \(a_{70}=+0.516112134\)
\(a_{71}=-1.095115715\) \(a_{72}=+0.000000000\) \(a_{73}=-0.675686752\) \(a_{74}=+0.683248983\) \(a_{75}=+0.000000000\)
\(a_{76}=+0.179020274\) \(a_{77}=+0.219737542\) \(a_{78}=+0.000000000\) \(a_{79}=+1.724198350\) \(a_{80}=-0.416465180\)
\(a_{81}=+0.000000000\) \(a_{82}=+0.628867020\) \(a_{83}=+1.395480848\) \(a_{84}=+0.000000000\) \(a_{85}=+3.015276278\)
\(a_{86}=-0.588917467\) \(a_{87}=+0.000000000\) \(a_{88}=-0.177312311\) \(a_{89}=+0.692254620\) \(a_{90}=+0.000000000\)
\(a_{91}=+0.081690943\) \(a_{92}=-0.608929486\) \(a_{93}=+0.000000000\) \(a_{94}=+0.617714953\) \(a_{95}=-0.596445683\)
\(a_{96}=+0.000000000\) \(a_{97}=+1.341516563\) \(a_{98}=+0.571361181\) \(a_{99}=+0.000000000\) \(a_{100}=+0.887545967\)

Showing 100 of 306 available coefficients

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