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: \( 13.6249278537 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+0.000000000\) \(a_{4}=+0.500000000\) \(a_{5}=-1.332434235\)
\(a_{6}=+0.000000000\) \(a_{7}=-1.435608954\) \(a_{8}=-0.353553391\) \(a_{9}=+0.000000000\) \(a_{10}=+0.942173283\)
\(a_{11}=+0.129515857\) \(a_{12}=+0.000000000\) \(a_{13}=+0.853997944\) \(a_{14}=+1.015128826\) \(a_{15}=+0.000000000\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.894418774\) \(a_{18}=+0.000000000\) \(a_{19}=-1.334537463\) \(a_{20}=-0.666217117\)
\(a_{21}=+0.000000000\) \(a_{22}=-0.091581541\) \(a_{23}=+0.469896842\) \(a_{24}=+0.000000000\) \(a_{25}=+0.775380990\)
\(a_{26}=-0.603867738\) \(a_{27}=+0.000000000\) \(a_{28}=-0.717804477\) \(a_{29}=+0.239071592\) \(a_{30}=+0.000000000\)
\(a_{31}=+0.886027757\) \(a_{32}=-0.176776695\) \(a_{33}=+0.000000000\) \(a_{34}=-1.339556361\) \(a_{35}=+1.912854517\)
\(a_{36}=+0.000000000\) \(a_{37}=-1.057877918\) \(a_{38}=+0.943660490\) \(a_{39}=+0.000000000\) \(a_{40}=+0.471086641\)
\(a_{41}=-0.519010460\) \(a_{42}=+0.000000000\) \(a_{43}=+1.664497010\) \(a_{44}=+0.064757928\) \(a_{45}=+0.000000000\)
\(a_{46}=-0.332267244\) \(a_{47}=+1.156790609\) \(a_{48}=+0.000000000\) \(a_{49}=+1.060973067\) \(a_{50}=-0.548277156\)
\(a_{51}=+0.000000000\) \(a_{52}=+0.426998972\) \(a_{53}=+0.949079551\) \(a_{54}=+0.000000000\) \(a_{55}=-0.172571361\)
\(a_{56}=+0.507564413\) \(a_{57}=+0.000000000\) \(a_{58}=-0.169049144\) \(a_{59}=-0.280801879\) \(a_{60}=+0.000000000\)
\(a_{61}=-0.836620028\) \(a_{62}=-0.626516235\) \(a_{63}=+0.000000000\) \(a_{64}=+0.125000000\) \(a_{65}=-1.137896097\)
\(a_{66}=+0.000000000\) \(a_{67}=-1.626466850\) \(a_{68}=+0.947209387\) \(a_{69}=+0.000000000\) \(a_{70}=-1.352592401\)
\(a_{71}=+0.437164039\) \(a_{72}=+0.000000000\) \(a_{73}=-1.548990509\) \(a_{74}=+0.748032649\) \(a_{75}=+0.000000000\)
\(a_{76}=-0.667268732\) \(a_{77}=-0.185934123\) \(a_{78}=+0.000000000\) \(a_{79}=+0.039796197\) \(a_{80}=-0.333108559\)
\(a_{81}=+0.000000000\) \(a_{82}=+0.366995816\) \(a_{83}=+0.854646521\) \(a_{84}=+0.000000000\) \(a_{85}=-2.524188429\)
\(a_{86}=-1.176977123\) \(a_{87}=+0.000000000\) \(a_{88}=-0.045790770\) \(a_{89}=-1.397638737\) \(a_{90}=+0.000000000\)
\(a_{91}=-1.226007095\) \(a_{92}=+0.234948421\) \(a_{93}=+0.000000000\) \(a_{94}=-0.817974484\) \(a_{95}=+1.778183403\)
\(a_{96}=+0.000000000\) \(a_{97}=+1.125117128\) \(a_{98}=-0.750221251\) \(a_{99}=+0.000000000\) \(a_{100}=+0.387690495\)

Showing 100 of 292 available coefficients

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