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: \( 10.9709627626 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+0.000000000\) \(a_{4}=+0.500000000\) \(a_{5}=+1.219345733\)
\(a_{6}=+0.000000000\) \(a_{7}=+0.346046023\) \(a_{8}=-0.353553391\) \(a_{9}=+0.000000000\) \(a_{10}=-0.862207636\)
\(a_{11}=-1.196902029\) \(a_{12}=+0.000000000\) \(a_{13}=+0.006720181\) \(a_{14}=-0.244691490\) \(a_{15}=+0.000000000\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.568209747\) \(a_{18}=+0.000000000\) \(a_{19}=-1.819468132\) \(a_{20}=+0.609672866\)
\(a_{21}=+0.000000000\) \(a_{22}=+0.846337541\) \(a_{23}=+1.601927244\) \(a_{24}=+0.000000000\) \(a_{25}=+0.486804017\)
\(a_{26}=-0.004751886\) \(a_{27}=+0.000000000\) \(a_{28}=+0.173023012\) \(a_{29}=+0.359544637\) \(a_{30}=+0.000000000\)
\(a_{31}=+1.000242196\) \(a_{32}=-0.176776695\) \(a_{33}=+0.000000000\) \(a_{34}=+0.401784965\) \(a_{35}=+0.421949742\)
\(a_{36}=+0.000000000\) \(a_{37}=-1.512957947\) \(a_{38}=+1.286558254\) \(a_{39}=+0.000000000\) \(a_{40}=-0.431103818\)
\(a_{41}=-0.552478014\) \(a_{42}=+0.000000000\) \(a_{43}=-1.416313762\) \(a_{44}=-0.598451015\) \(a_{45}=+0.000000000\)
\(a_{46}=-1.132733617\) \(a_{47}=-0.368096561\) \(a_{48}=+0.000000000\) \(a_{49}=-0.880252150\) \(a_{50}=-0.344222421\)
\(a_{51}=+0.000000000\) \(a_{52}=+0.003360091\) \(a_{53}=+1.366788753\) \(a_{54}=+0.000000000\) \(a_{55}=-1.459437382\)
\(a_{56}=-0.122345745\) \(a_{57}=+0.000000000\) \(a_{58}=-0.254236451\) \(a_{59}=+0.675327142\) \(a_{60}=+0.000000000\)
\(a_{61}=-1.851003914\) \(a_{62}=-0.707278040\) \(a_{63}=+0.000000000\) \(a_{64}=+0.125000000\) \(a_{65}=+0.008194224\)
\(a_{66}=+0.000000000\) \(a_{67}=+1.329556060\) \(a_{68}=-0.284104874\) \(a_{69}=+0.000000000\) \(a_{70}=-0.298363524\)
\(a_{71}=-1.345345943\) \(a_{72}=+0.000000000\) \(a_{73}=-0.909921466\) \(a_{74}=+1.069822824\) \(a_{75}=+0.000000000\)
\(a_{76}=-0.909734066\) \(a_{77}=-0.414183188\) \(a_{78}=+0.000000000\) \(a_{79}=+0.392577929\) \(a_{80}=+0.304836433\)
\(a_{81}=+0.000000000\) \(a_{82}=+0.390660950\) \(a_{83}=+1.256661196\) \(a_{84}=+0.000000000\) \(a_{85}=-0.692844131\)
\(a_{86}=+1.001485065\) \(a_{87}=+0.000000000\) \(a_{88}=+0.423168771\) \(a_{89}=-1.475840472\) \(a_{90}=+0.000000000\)
\(a_{91}=+0.002325492\) \(a_{92}=+0.800963622\) \(a_{93}=+0.000000000\) \(a_{94}=+0.260283575\) \(a_{95}=-2.218560703\)
\(a_{96}=+0.000000000\) \(a_{97}=-0.184930175\) \(a_{98}=+0.622432264\) \(a_{99}=+0.000000000\) \(a_{100}=+0.243402008\)

Showing 100 of 268 available coefficients

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