Properties

Level $69$
Weight $0$
Character 69.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 69 = 3 \cdot 23 \)
Weight: \( 0 \)
Character: 69.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 2.8876538 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.213358382\) \(a_{3}=-0.577350269\) \(a_{4}=+0.472238563\) \(a_{5}=-0.568688490\)
\(a_{6}=+0.700532788\) \(a_{7}=-0.570123770\) \(a_{8}=+0.640363763\) \(a_{9}=+0.333333333\) \(a_{10}=+0.690022946\)
\(a_{11}=-1.167350690\) \(a_{12}=-0.272647062\) \(a_{13}=-1.587310380\) \(a_{14}=+0.691764455\) \(a_{15}=+0.328332453\)
\(a_{16}=-1.249229303\) \(a_{17}=+1.898264810\) \(a_{18}=-0.404452794\) \(a_{19}=+0.926442450\) \(a_{20}=-0.268556635\)
\(a_{21}=+0.329161112\) \(a_{22}=+1.416414744\) \(a_{23}=-0.208514414\) \(a_{24}=-0.369714191\) \(a_{25}=-0.676593401\)
\(a_{26}=+1.925976354\) \(a_{27}=-0.192450090\) \(a_{28}=-0.269234430\) \(a_{29}=+1.706105700\) \(a_{30}=-0.398384934\)
\(a_{31}=-0.471181680\) \(a_{32}=+0.875399082\) \(a_{33}=+0.673970235\) \(a_{34}=-2.303275518\) \(a_{35}=+0.324222826\)
\(a_{36}=+0.157412854\) \(a_{37}=-0.380688820\) \(a_{38}=-1.124106712\) \(a_{39}=+0.916434075\) \(a_{40}=-0.364167501\)
\(a_{41}=-0.481984900\) \(a_{42}=-0.399390394\) \(a_{43}=+0.926885970\) \(a_{44}=-0.551268013\) \(a_{45}=-0.189562830\)
\(a_{46}=+0.253002712\) \(a_{47}=-0.307229660\) \(a_{48}=+0.721242874\) \(a_{49}=-0.674958887\) \(a_{50}=+0.820950275\)
\(a_{51}=-1.095963699\) \(a_{52}=-0.749589173\) \(a_{53}=+0.217916100\) \(a_{54}=+0.233510929\) \(a_{55}=+0.663858901\)
\(a_{56}=-0.365086603\) \(a_{57}=-0.534881798\) \(a_{58}=-2.070117652\) \(a_{59}=+0.427483460\) \(a_{60}=+0.155051246\)
\(a_{61}=+1.679697080\) \(a_{62}=+0.571712241\) \(a_{63}=-0.190041257\) \(a_{64}=+0.187056489\) \(a_{65}=+0.902685143\)
\(a_{66}=-0.817767434\) \(a_{67}=+0.221014370\) \(a_{68}=+0.896433846\) \(a_{69}=+0.120385853\) \(a_{70}=-0.393398483\)
\(a_{71}=+0.419557910\) \(a_{72}=+0.213454588\) \(a_{73}=-0.278191050\) \(a_{74}=+0.461911971\) \(a_{75}=+0.390631382\)
\(a_{76}=+0.437501851\) \(a_{77}=+0.665534376\) \(a_{78}=-1.111962967\) \(a_{79}=+1.241387508\) \(a_{80}=+0.710422326\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.584820418\) \(a_{83}=-1.765250920\) \(a_{84}=+0.155442571\) \(a_{85}=-1.079521348\)
\(a_{86}=-1.124644861\) \(a_{87}=-0.985020585\) \(a_{88}=-0.747529081\) \(a_{89}=-0.308409810\) \(a_{90}=+0.230007649\)
\(a_{91}=+0.904963378\) \(a_{92}=-0.098468547\) \(a_{93}=+0.272036870\) \(a_{94}=+0.372779683\) \(a_{95}=-0.526857158\)
\(a_{96}=-0.505411896\) \(a_{97}=+0.101855130\) \(a_{98}=+0.818967023\) \(a_{99}=-0.389116897\) \(a_{100}=-0.319513496\)

Showing 100 of 418 available coefficients

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