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: \( 13.4099687635 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+0.000000000\) \(a_{4}=+0.500000000\) \(a_{5}=-0.239846582\)
\(a_{6}=+0.000000000\) \(a_{7}=+0.149202504\) \(a_{8}=-0.353553391\) \(a_{9}=+0.000000000\) \(a_{10}=+0.169597145\)
\(a_{11}=-0.187845798\) \(a_{12}=+0.000000000\) \(a_{13}=-0.162194603\) \(a_{14}=-0.105502102\) \(a_{15}=+0.000000000\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.615588981\) \(a_{18}=+0.000000000\) \(a_{19}=+1.119538031\) \(a_{20}=-0.119923291\)
\(a_{21}=+0.000000000\) \(a_{22}=+0.132827038\) \(a_{23}=+1.149595640\) \(a_{24}=+0.000000000\) \(a_{25}=-0.942473617\)
\(a_{26}=+0.114688904\) \(a_{27}=+0.000000000\) \(a_{28}=+0.074601252\) \(a_{29}=-1.311615284\) \(a_{30}=+0.000000000\)
\(a_{31}=+1.231792461\) \(a_{32}=-0.176776695\) \(a_{33}=+0.000000000\) \(a_{34}=+0.435287143\) \(a_{35}=-0.035785711\)
\(a_{36}=+0.000000000\) \(a_{37}=-0.458029894\) \(a_{38}=-0.791632933\) \(a_{39}=+0.000000000\) \(a_{40}=+0.084798572\)
\(a_{41}=-1.336438292\) \(a_{42}=+0.000000000\) \(a_{43}=-0.602304695\) \(a_{44}=-0.093922899\) \(a_{45}=+0.000000000\)
\(a_{46}=-0.812886873\) \(a_{47}=-0.413346852\) \(a_{48}=+0.000000000\) \(a_{49}=-0.977738613\) \(a_{50}=+0.666429486\)
\(a_{51}=+0.000000000\) \(a_{52}=-0.081097302\) \(a_{53}=-0.023767922\) \(a_{54}=+0.000000000\) \(a_{55}=+0.045054173\)
\(a_{56}=-0.052751051\) \(a_{57}=+0.000000000\) \(a_{58}=+0.927452062\) \(a_{59}=-0.311127685\) \(a_{60}=+0.000000000\)
\(a_{61}=+1.446854412\) \(a_{62}=-0.871008802\) \(a_{63}=+0.000000000\) \(a_{64}=+0.125000000\) \(a_{65}=+0.038901821\)
\(a_{66}=+0.000000000\) \(a_{67}=+1.390203851\) \(a_{68}=-0.307794491\) \(a_{69}=+0.000000000\) \(a_{70}=+0.025304319\)
\(a_{71}=+1.420568917\) \(a_{72}=+0.000000000\) \(a_{73}=+1.711529859\) \(a_{74}=+0.323876044\) \(a_{75}=+0.000000000\)
\(a_{76}=+0.559769015\) \(a_{77}=-0.028027063\) \(a_{78}=+0.000000000\) \(a_{79}=+1.440748277\) \(a_{80}=-0.059961646\)
\(a_{81}=+0.000000000\) \(a_{82}=+0.945004579\) \(a_{83}=-1.403064381\) \(a_{84}=+0.000000000\) \(a_{85}=+0.147646913\)
\(a_{86}=+0.425893734\) \(a_{87}=+0.000000000\) \(a_{88}=+0.066413519\) \(a_{89}=-0.744340502\) \(a_{90}=+0.000000000\)
\(a_{91}=-0.024199841\) \(a_{92}=+0.574797820\) \(a_{93}=+0.000000000\) \(a_{94}=+0.292280362\) \(a_{95}=-0.268517370\)
\(a_{96}=+0.000000000\) \(a_{97}=+1.232141915\) \(a_{98}=+0.691365603\) \(a_{99}=+0.000000000\) \(a_{100}=-0.471236809\)

Showing 100 of 292 available coefficients

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