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: \( 17.0312699717 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+0.000000000\) \(a_{4}=+0.500000000\) \(a_{5}=+1.548902435\)
\(a_{6}=+0.000000000\) \(a_{7}=-0.075193006\) \(a_{8}=-0.353553391\) \(a_{9}=+0.000000000\) \(a_{10}=-1.095239415\)
\(a_{11}=+1.060694140\) \(a_{12}=+0.000000000\) \(a_{13}=-1.155612263\) \(a_{14}=+0.053169484\) \(a_{15}=+0.000000000\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.254663955\) \(a_{18}=+0.000000000\) \(a_{19}=-0.456429865\) \(a_{20}=+0.774451217\)
\(a_{21}=+0.000000000\) \(a_{22}=-0.750024019\) \(a_{23}=+1.856168589\) \(a_{24}=+0.000000000\) \(a_{25}=+1.399098753\)
\(a_{26}=+0.817141268\) \(a_{27}=+0.000000000\) \(a_{28}=-0.037596503\) \(a_{29}=+0.618933533\) \(a_{30}=+0.000000000\)
\(a_{31}=-0.364234082\) \(a_{32}=-0.176776695\) \(a_{33}=+0.000000000\) \(a_{34}=+0.887181391\) \(a_{35}=-0.116466629\)
\(a_{36}=+0.000000000\) \(a_{37}=+0.508846542\) \(a_{38}=+0.322744653\) \(a_{39}=+0.000000000\) \(a_{40}=-0.547619708\)
\(a_{41}=+1.202597154\) \(a_{42}=+0.000000000\) \(a_{43}=+1.720975495\) \(a_{44}=+0.530347070\) \(a_{45}=+0.000000000\)
\(a_{46}=-1.312509396\) \(a_{47}=-0.954571016\) \(a_{48}=+0.000000000\) \(a_{49}=-0.994346012\) \(a_{50}=-0.989312216\)
\(a_{51}=+0.000000000\) \(a_{52}=-0.577806132\) \(a_{53}=+0.130333428\) \(a_{54}=+0.000000000\) \(a_{55}=+1.642911737\)
\(a_{56}=+0.026584742\) \(a_{57}=+0.000000000\) \(a_{58}=-0.437652099\) \(a_{59}=-1.328061818\) \(a_{60}=+0.000000000\)
\(a_{61}=+1.221661397\) \(a_{62}=+0.257552389\) \(a_{63}=+0.000000000\) \(a_{64}=+0.125000000\) \(a_{65}=-1.789930648\)
\(a_{66}=+0.000000000\) \(a_{67}=+0.408405654\) \(a_{68}=-0.627331978\) \(a_{69}=+0.000000000\) \(a_{70}=+0.082354343\)
\(a_{71}=+0.594778461\) \(a_{72}=+0.000000000\) \(a_{73}=-1.574661522\) \(a_{74}=-0.359808840\) \(a_{75}=+0.000000000\)
\(a_{76}=-0.228214933\) \(a_{77}=-0.079756780\) \(a_{78}=+0.000000000\) \(a_{79}=+0.500813912\) \(a_{80}=+0.387225609\)
\(a_{81}=+0.000000000\) \(a_{82}=-0.850364603\) \(a_{83}=+0.570777738\) \(a_{84}=+0.000000000\) \(a_{85}=-1.943352056\)
\(a_{86}=-1.216913443\) \(a_{87}=+0.000000000\) \(a_{88}=-0.375012010\) \(a_{89}=-1.243923906\) \(a_{90}=+0.000000000\)
\(a_{91}=+0.086893959\) \(a_{92}=+0.928084294\) \(a_{93}=+0.000000000\) \(a_{94}=+0.674983639\) \(a_{95}=-0.706965330\)
\(a_{96}=+0.000000000\) \(a_{97}=+1.159725437\) \(a_{98}=+0.703108808\) \(a_{99}=+0.000000000\) \(a_{100}=+0.699549376\)

Showing 100 of 330 available coefficients

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