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: \( 7.60781292346 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+0.000000000\) \(a_{4}=+0.500000000\) \(a_{5}=-1.757148071\)
\(a_{6}=+0.000000000\) \(a_{7}=+1.187885305\) \(a_{8}=+0.353553391\) \(a_{9}=+0.000000000\) \(a_{10}=-1.242491317\)
\(a_{11}=+0.388303486\) \(a_{12}=+0.000000000\) \(a_{13}=+0.147178083\) \(a_{14}=+0.839961754\) \(a_{15}=+0.000000000\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.709613193\) \(a_{18}=+0.000000000\) \(a_{19}=+1.720886710\) \(a_{20}=-0.878574036\)
\(a_{21}=+0.000000000\) \(a_{22}=+0.274572028\) \(a_{23}=-0.009425853\) \(a_{24}=+0.000000000\) \(a_{25}=+2.087569344\)
\(a_{26}=+0.104070621\) \(a_{27}=+0.000000000\) \(a_{28}=+0.593942652\) \(a_{29}=+1.207327067\) \(a_{30}=+0.000000000\)
\(a_{31}=-0.794884135\) \(a_{32}=+0.176776695\) \(a_{33}=+0.000000000\) \(a_{34}=+0.501772301\) \(a_{35}=-2.087290372\)
\(a_{36}=+0.000000000\) \(a_{37}=+1.731999830\) \(a_{38}=+1.216850662\) \(a_{39}=+0.000000000\) \(a_{40}=-0.621245658\)
\(a_{41}=-0.970026953\) \(a_{42}=+0.000000000\) \(a_{43}=-0.420949994\) \(a_{44}=+0.194151743\) \(a_{45}=+0.000000000\)
\(a_{46}=-0.006665085\) \(a_{47}=+0.594622147\) \(a_{48}=+0.000000000\) \(a_{49}=+0.411071497\) \(a_{50}=+1.476134439\)
\(a_{51}=+0.000000000\) \(a_{52}=+0.073589042\) \(a_{53}=-0.991737630\) \(a_{54}=+0.000000000\) \(a_{55}=-0.682306722\)
\(a_{56}=+0.419980877\) \(a_{57}=+0.000000000\) \(a_{58}=+0.853709157\) \(a_{59}=-1.170882840\) \(a_{60}=+0.000000000\)
\(a_{61}=+0.330757298\) \(a_{62}=-0.562067962\) \(a_{63}=+0.000000000\) \(a_{64}=+0.125000000\) \(a_{65}=-0.258613685\)
\(a_{66}=+0.000000000\) \(a_{67}=-0.817540405\) \(a_{68}=+0.354806596\) \(a_{69}=+0.000000000\) \(a_{70}=-1.475937176\)
\(a_{71}=+0.086370099\) \(a_{72}=+0.000000000\) \(a_{73}=+0.978259359\) \(a_{74}=+1.224708825\) \(a_{75}=+0.000000000\)
\(a_{76}=+0.860443355\) \(a_{77}=+0.461260005\) \(a_{78}=+0.000000000\) \(a_{79}=+1.148308219\) \(a_{80}=-0.439287018\)
\(a_{81}=+0.000000000\) \(a_{82}=-0.685912636\) \(a_{83}=+0.282019214\) \(a_{84}=+0.000000000\) \(a_{85}=-1.246895453\)
\(a_{86}=-0.297656595\) \(a_{87}=+0.000000000\) \(a_{88}=+0.137286014\) \(a_{89}=+0.237822475\) \(a_{90}=+0.000000000\)
\(a_{91}=+0.174830682\) \(a_{92}=-0.004712927\) \(a_{93}=+0.000000000\) \(a_{94}=+0.420461352\) \(a_{95}=-3.023852762\)
\(a_{96}=+0.000000000\) \(a_{97}=-0.785488897\) \(a_{98}=+0.290671443\) \(a_{99}=+0.000000000\) \(a_{100}=+1.043784672\)

Showing 100 of 192 available coefficients

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