Properties

Level $33$
Weight $0$
Character 33.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 33 = 3 \cdot 11 \)
Weight: \( 0 \)
Character: 33.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 1.29767492872 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.124903268\) \(a_{3}=+0.577350269\) \(a_{4}=+0.265407363\) \(a_{5}=-1.173354446\)
\(a_{6}=-0.649463206\) \(a_{7}=+1.292624997\) \(a_{8}=+0.826345658\) \(a_{9}=+0.333333333\) \(a_{10}=+1.319910251\)
\(a_{11}=+0.301511348\) \(a_{12}=+0.153233013\) \(a_{13}=-0.762621476\) \(a_{14}=-1.454078085\) \(a_{15}=-0.677436506\)
\(a_{16}=-1.194966297\) \(a_{17}=+1.242443703\) \(a_{18}=-0.374967753\) \(a_{19}=-0.353423877\) \(a_{20}=-0.311416911\)
\(a_{21}=+0.746297389\) \(a_{22}=-0.339171091\) \(a_{23}=-0.678538582\) \(a_{24}=+0.477090886\) \(a_{25}=+0.376760658\)
\(a_{26}=+0.857875388\) \(a_{27}=+0.192450071\) \(a_{28}=+0.343072188\) \(a_{29}=-0.340583376\) \(a_{30}=+0.762050554\)
\(a_{31}=+0.695947441\) \(a_{32}=+0.517875826\) \(a_{33}=+0.174077657\) \(a_{34}=-1.397628994\) \(a_{35}=-1.516707259\)
\(a_{36}=+0.088469124\) \(a_{37}=+1.124128315\) \(a_{38}=+0.397567651\) \(a_{39}=-0.440299708\) \(a_{40}=-0.969596371\)
\(a_{41}=+1.447910621\) \(a_{42}=-0.839512322\) \(a_{43}=-0.114547119\) \(a_{44}=+0.080023294\) \(a_{45}=-0.391118155\)
\(a_{46}=+0.763290273\) \(a_{47}=-0.088029119\) \(a_{48}=-0.689914099\) \(a_{49}=+0.670879393\) \(a_{50}=-0.423819234\)
\(a_{51}=+0.717325170\) \(a_{52}=-0.202405351\) \(a_{53}=-0.877146139\) \(a_{54}=-0.216487725\) \(a_{55}=-0.353779722\)
\(a_{56}=+1.068155072\) \(a_{57}=-0.204049372\) \(a_{58}=+0.383123363\) \(a_{59}=-1.099446287\) \(a_{60}=-0.179796632\)
\(a_{61}=-1.421028090\) \(a_{62}=-0.782873550\) \(a_{63}=+0.430874965\) \(a_{64}=+0.612406092\) \(a_{65}=+0.894825336\)
\(a_{66}=-0.195820505\) \(a_{67}=+0.352071396\) \(a_{68}=+0.329753703\) \(a_{69}=-0.391754478\) \(a_{70}=+1.706148990\)
\(a_{71}=-0.745615533\) \(a_{72}=+0.275448504\) \(a_{73}=+1.700628796\) \(a_{74}=-1.264535674\) \(a_{75}=+0.217522841\)
\(a_{76}=-0.093801259\) \(a_{77}=+0.389741133\) \(a_{78}=+0.495294566\) \(a_{79}=+0.182409234\) \(a_{80}=+1.402119019\)
\(a_{81}=+0.111111075\) \(a_{82}=-1.628759388\) \(a_{83}=+0.527486602\) \(a_{84}=+0.198072790\) \(a_{85}=-1.457826866\)
\(a_{86}=+0.128854411\) \(a_{87}=-0.196635868\) \(a_{88}=+0.249152630\) \(a_{89}=-0.157763132\) \(a_{90}=+0.439970097\)
\(a_{91}=-0.985783595\) \(a_{92}=-0.180089163\) \(a_{93}=+0.401805468\) \(a_{94}=+0.099024275\) \(a_{95}=+0.414691489\)
\(a_{96}=+0.298995736\) \(a_{97}=-0.041911062\) \(a_{98}=-0.754674432\) \(a_{99}=+0.100503816\) \(a_{100}=+0.099995097\)

Showing 100 of 2000 available coefficients

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