Properties

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

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Maass form invariants

Level: \( 3 \)
Weight: \( 0 \)
Character: 3.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 14.7873247385 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.816597996\) \(a_{3}=-0.577350269\) \(a_{4}=-0.333167713\) \(a_{5}=+1.485961564\)
\(a_{6}=-0.471463073\) \(a_{7}=-0.572848968\) \(a_{8}=-1.088662083\) \(a_{9}=+0.333333333\) \(a_{10}=+1.213433236\)
\(a_{11}=-1.107948890\) \(a_{12}=+0.192354470\) \(a_{13}=-1.042597057\) \(a_{14}=-0.467787282\) \(a_{15}=-0.857920487\)
\(a_{16}=-0.555830692\) \(a_{17}=-1.188618265\) \(a_{18}=+0.272221528\) \(a_{19}=+0.083839999\) \(a_{20}=-0.495074415\)
\(a_{21}=+0.330734506\) \(a_{22}=-0.904748843\) \(a_{23}=-0.540634236\) \(a_{24}=+0.628539347\) \(a_{25}=+1.208081770\)
\(a_{26}=-0.851382661\) \(a_{27}=-0.192450090\) \(a_{28}=+0.190854780\) \(a_{29}=-0.686644494\) \(a_{30}=-0.700576005\)
\(a_{31}=+1.141217170\) \(a_{32}=+0.634771142\) \(a_{33}=+0.639674590\) \(a_{34}=-0.970619767\) \(a_{35}=-0.851231548\)
\(a_{36}=-0.111055904\) \(a_{37}=+0.530195120\) \(a_{38}=+0.068463575\) \(a_{39}=+0.601943687\) \(a_{40}=-1.617710011\)
\(a_{41}=+1.713464963\) \(a_{42}=+0.270077135\) \(a_{43}=-1.169605356\) \(a_{44}=+0.369132797\) \(a_{45}=+0.495320521\)
\(a_{46}=-0.441480833\) \(a_{47}=-0.926034961\) \(a_{48}=+0.320909502\) \(a_{49}=-0.671844061\) \(a_{50}=+0.986517153\)
\(a_{51}=+0.686246584\) \(a_{52}=+0.347359674\) \(a_{53}=+0.176598487\) \(a_{54}=-0.157154359\) \(a_{55}=-1.646369454\)
\(a_{56}=+0.623638961\) \(a_{57}=-0.048405069\) \(a_{58}=-0.560712553\) \(a_{59}=-0.304110160\) \(a_{60}=+0.285831454\)
\(a_{61}=+0.615373045\) \(a_{62}=+0.931915360\) \(a_{63}=-0.190949681\) \(a_{64}=+1.074185069\) \(a_{65}=-1.549259141\)
\(a_{66}=+0.522356988\) \(a_{67}=-1.477258259\) \(a_{68}=+0.396007790\) \(a_{69}=+0.312135321\) \(a_{70}=-0.695113977\)
\(a_{71}=+0.288029619\) \(a_{72}=-0.362887360\) \(a_{73}=+1.187391125\) \(a_{74}=+0.432956271\) \(a_{75}=-0.697486336\)
\(a_{76}=-0.027932779\) \(a_{77}=+0.634687381\) \(a_{78}=+0.491546007\) \(a_{79}=-1.017961032\) \(a_{80}=-0.825944339\)
\(a_{81}=+0.111111120\) \(a_{82}=+1.399212062\) \(a_{83}=-0.042146071\) \(a_{84}=-0.110190076\) \(a_{85}=-1.766234634\)
\(a_{86}=-0.955097359\) \(a_{87}=+0.396434394\) \(a_{88}=+1.206181902\) \(a_{89}=+0.867231899\) \(a_{90}=+0.404477788\)
\(a_{91}=+0.597250742\) \(a_{92}=+0.180121861\) \(a_{93}=-0.658882201\) \(a_{94}=-0.756198379\) \(a_{95}=+0.124583224\)
\(a_{96}=-0.366485029\) \(a_{97}=-0.084787036\) \(a_{98}=-0.548627022\) \(a_{99}=-0.369316326\) \(a_{100}=-0.402493033\)

Showing 100 of 5000 available coefficients

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