Properties

Level $3$
Weight $0$
Character 3.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 3 \)
Weight: \( 0 \)
Character: 3.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 11.3464186204 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.816369830\) \(a_{3}=-0.577350269\) \(a_{4}=-0.333540300\) \(a_{5}=-1.748608080\)
\(a_{6}=+0.471331341\) \(a_{7}=+0.160684992\) \(a_{8}=+1.088662069\) \(a_{9}=+0.333333332\) \(a_{10}=+1.427510889\)
\(a_{11}=-0.399082451\) \(a_{12}=+0.192569745\) \(a_{13}=+0.240646991\) \(a_{14}=-0.131174289\) \(a_{15}=+1.009538213\)
\(a_{16}=-0.555106916\) \(a_{17}=-0.516016084\) \(a_{18}=-0.272123277\) \(a_{19}=+0.609694574\) \(a_{20}=+0.583231264\)
\(a_{21}=-0.092771524\) \(a_{22}=+0.325798845\) \(a_{23}=-1.590675122\) \(a_{24}=-0.628539338\) \(a_{25}=+2.057630217\)
\(a_{26}=-0.196457602\) \(a_{27}=-0.192450090\) \(a_{28}=-0.053594921\) \(a_{29}=+0.268561167\) \(a_{30}=-0.824173792\)
\(a_{31}=+0.485886695\) \(a_{32}=-0.635404912\) \(a_{33}=+0.230410341\) \(a_{34}=+0.421259963\) \(a_{35}=-0.280975076\)
\(a_{36}=-0.111180100\) \(a_{37}=+1.527991194\) \(a_{38}=-0.497736256\) \(a_{39}=-0.138938071\) \(a_{40}=-1.903643289\)
\(a_{41}=+0.674676221\) \(a_{42}=+0.075735873\) \(a_{43}=+0.452902487\) \(a_{44}=+0.133110069\) \(a_{45}=-0.582869360\)
\(a_{46}=+1.298579180\) \(a_{47}=+0.326047372\) \(a_{48}=+0.320550970\) \(a_{49}=-0.974180332\) \(a_{50}=-1.679787229\)
\(a_{51}=+0.297922024\) \(a_{52}=-0.080265743\) \(a_{53}=+0.683909630\) \(a_{54}=+0.157110460\) \(a_{55}=+0.697838741\)
\(a_{56}=+0.174931639\) \(a_{57}=-0.352007354\) \(a_{58}=-0.219245196\) \(a_{59}=+0.758457873\) \(a_{60}=-0.336728784\)
\(a_{61}=-0.845483641\) \(a_{62}=-0.396663301\) \(a_{63}=+0.053561664\) \(a_{64}=+1.073935968\) \(a_{65}=-0.420798683\)
\(a_{66}=-0.188100050\) \(a_{67}=-0.807609445\) \(a_{68}=+0.172112159\) \(a_{69}=+0.918376711\) \(a_{70}=+0.229379578\)
\(a_{71}=+0.396120899\) \(a_{72}=+0.362887353\) \(a_{73}=+0.788272981\) \(a_{74}=-1.247405907\) \(a_{75}=-1.187973354\)
\(a_{76}=-0.203357716\) \(a_{77}=-0.064126566\) \(a_{78}=+0.113424850\) \(a_{79}=-0.559648354\) \(a_{80}=+0.970845693\)
\(a_{81}=+0.111111089\) \(a_{82}=-0.550785335\) \(a_{83}=+1.368192670\) \(a_{84}=+0.030943089\) \(a_{85}=+0.902309889\)
\(a_{86}=-0.369736005\) \(a_{87}=-0.155053893\) \(a_{88}=-0.434465788\) \(a_{89}=-1.677435211\) \(a_{90}=+0.475836859\)
\(a_{91}=+0.038668258\) \(a_{92}=+0.530554301\) \(a_{93}=-0.280526443\) \(a_{94}=-0.266175076\) \(a_{95}=-1.066117375\)
\(a_{96}=+0.366850655\) \(a_{97}=+1.771692866\) \(a_{98}=+0.795292545\) \(a_{99}=-0.133027597\) \(a_{100}=-0.686304533\)

Showing 100 of 5000 available coefficients

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