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: \( 23.9798500362 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.184472059\) \(a_{3}=-0.577350269\) \(a_{4}=-0.965970059\) \(a_{5}=+1.053913566\)
\(a_{6}=+0.106504993\) \(a_{7}=+1.429651556\) \(a_{8}=+0.362666545\) \(a_{9}=+0.333333333\) \(a_{10}=-0.194417605\)
\(a_{11}=-1.050228208\) \(a_{12}=+0.557703074\) \(a_{13}=-1.188829399\) \(a_{14}=-0.263730766\) \(a_{15}=-0.608477281\)
\(a_{16}=+0.899068215\) \(a_{17}=-0.494552779\) \(a_{18}=-0.061490686\) \(a_{19}=+0.278957770\) \(a_{20}=-1.018048950\)
\(a_{21}=-0.825409711\) \(a_{22}=+0.193737760\) \(a_{23}=+1.394734269\) \(a_{24}=-0.209385627\) \(a_{25}=+0.110733805\)
\(a_{26}=+0.219305807\) \(a_{27}=-0.192450090\) \(a_{28}=-1.381000599\) \(a_{29}=+0.607723075\) \(a_{30}=+0.112247057\)
\(a_{31}=-1.636919950\) \(a_{32}=-0.528519509\) \(a_{33}=+0.606349539\) \(a_{34}=+0.091231169\) \(a_{35}=+1.506729170\)
\(a_{36}=-0.321990020\) \(a_{37}=+1.200873669\) \(a_{38}=-0.051459914\) \(a_{39}=+0.686370974\) \(a_{40}=+0.382219191\)
\(a_{41}=+1.444181526\) \(a_{42}=+0.152265029\) \(a_{43}=+0.520907865\) \(a_{44}=+1.014489005\) \(a_{45}=+0.351304522\)
\(a_{46}=-0.257289502\) \(a_{47}=+0.125448536\) \(a_{48}=-0.519077276\) \(a_{49}=+1.043903572\) \(a_{50}=-0.020427293\)
\(a_{51}=+0.285530180\) \(a_{52}=+1.148373605\) \(a_{53}=-0.438067969\) \(a_{54}=+0.035501664\) \(a_{55}=-1.106849756\)
\(a_{56}=+0.518486790\) \(a_{57}=-0.161056344\) \(a_{58}=-0.112107927\) \(a_{59}=+0.093961119\) \(a_{60}=+0.587770835\)
\(a_{61}=+0.250608209\) \(a_{62}=+0.301965993\) \(a_{63}=+0.476550519\) \(a_{64}=-0.801571133\) \(a_{65}=-1.252923431\)
\(a_{66}=-0.111854548\) \(a_{67}=+1.072830701\) \(a_{68}=+0.477723177\) \(a_{69}=-0.805250206\) \(a_{70}=-0.277949432\)
\(a_{71}=+0.154251458\) \(a_{72}=+0.120888848\) \(a_{73}=+1.466136333\) \(a_{74}=-0.221527638\) \(a_{75}=-0.063932192\)
\(a_{76}=-0.269464854\) \(a_{77}=-1.501460392\) \(a_{78}=-0.126616267\) \(a_{79}=-0.010385137\) \(a_{80}=+0.947540189\)
\(a_{81}=+0.111111111\) \(a_{82}=-0.266411140\) \(a_{83}=+0.306215828\) \(a_{84}=+0.797321067\) \(a_{85}=-0.521215883\)
\(a_{86}=-0.096092946\) \(a_{87}=-0.350869081\) \(a_{88}=-0.380882635\) \(a_{89}=+1.829368714\) \(a_{90}=-0.064805868\)
\(a_{91}=-1.699611800\) \(a_{92}=-1.347271545\) \(a_{93}=+0.945076174\) \(a_{94}=-0.023141750\) \(a_{95}=+0.293997378\)
\(a_{96}=+0.305140881\) \(a_{97}=+1.238376261\) \(a_{98}=-0.192571041\) \(a_{99}=-0.350076069\) \(a_{100}=-0.106965540\)

Showing 100 of 1228 available coefficients

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