Properties

Level $61$
Weight $0$
Character 61.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 61 \)
Weight: \( 0 \)
Character: 61.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 0.824033784121 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.188931235\) \(a_{3}=-1.498821735\) \(a_{4}=-0.964304988\) \(a_{5}=+1.244410466\)
\(a_{6}=-0.283174242\) \(a_{7}=-0.925409646\) \(a_{8}=-0.371118568\) \(a_{9}=+1.246466594\) \(a_{10}=+0.235108007\)
\(a_{11}=+0.999546750\) \(a_{12}=+1.445321276\) \(a_{13}=+0.891945506\) \(a_{14}=-0.174838788\) \(a_{15}=-1.865149454\)
\(a_{16}=+0.894189099\) \(a_{17}=-1.061739289\) \(a_{18}=+0.235496473\) \(a_{19}=-0.775120937\) \(a_{20}=-1.199991220\)
\(a_{21}=+1.387024092\) \(a_{22}=+0.188845602\) \(a_{23}=-0.674171712\) \(a_{24}=+0.556240576\) \(a_{25}=+0.548557408\)
\(a_{26}=+0.168516366\) \(a_{27}=-0.369409488\) \(a_{28}=+0.892377138\) \(a_{29}=-0.266523098\) \(a_{30}=-0.352384991\)
\(a_{31}=+0.649423653\) \(a_{32}=+0.540058819\) \(a_{33}=-1.498142394\) \(a_{34}=-0.200595715\) \(a_{35}=-1.151589449\)
\(a_{36}=-1.201973954\) \(a_{37}=+0.499196892\) \(a_{38}=-0.146444556\) \(a_{39}=-1.336867310\) \(a_{40}=-0.461823830\)
\(a_{41}=+1.107961841\) \(a_{42}=+0.262052175\) \(a_{43}=+1.135249757\) \(a_{44}=-0.963867917\) \(a_{45}=+1.551116075\)
\(a_{46}=-0.127372094\) \(a_{47}=+0.752458994\) \(a_{48}=-1.340230057\) \(a_{49}=-0.143616986\) \(a_{50}=+0.103639629\)
\(a_{51}=+1.591357923\) \(a_{52}=-0.860107500\) \(a_{53}=-1.712295334\) \(a_{54}=-0.069792991\) \(a_{55}=+1.243846437\)
\(a_{56}=+0.343436703\) \(a_{57}=+1.161768107\) \(a_{58}=-0.050354538\) \(a_{59}=+0.409363494\) \(a_{60}=+1.798572922\)
\(a_{61}=-0.128036880\) \(a_{62}=+0.122696413\) \(a_{63}=-1.153492210\) \(a_{64}=-0.792155119\) \(a_{65}=+1.109946322\)
\(a_{66}=-0.283045893\) \(a_{67}=-0.678138001\) \(a_{68}=+1.023840492\) \(a_{69}=+1.010463214\) \(a_{70}=-0.217571217\)
\(a_{71}=-0.649105565\) \(a_{72}=-0.462586898\) \(a_{73}=+1.431654779\) \(a_{74}=+0.094313886\) \(a_{75}=-0.822189766\)
\(a_{76}=+0.747452986\) \(a_{77}=-0.924990204\) \(a_{78}=-0.252575993\) \(a_{79}=-1.037018400\) \(a_{80}=+1.112738273\)
\(a_{81}=-0.692787624\) \(a_{82}=+0.209328599\) \(a_{83}=+0.324977516\) \(a_{84}=-1.337514251\) \(a_{85}=-1.321239483\)
\(a_{86}=+0.214484139\) \(a_{87}=+0.399470613\) \(a_{88}=-0.370950359\) \(a_{89}=-1.084689959\) \(a_{90}=+0.293054276\)
\(a_{91}=-0.825414975\) \(a_{92}=+0.650107144\) \(a_{93}=-0.973370287\) \(a_{94}=+0.142163007\) \(a_{95}=-0.964568606\)
\(a_{96}=-0.809451897\) \(a_{97}=+0.795826681\) \(a_{98}=-0.027133735\) \(a_{99}=+1.245901633\) \(a_{100}=-0.528976645\)

Showing 100 of 546 available coefficients

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