Properties

Level $2$
Weight $0$
Character 2.1
Symmetry even
Fricke sign $-1$

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Maass form invariants

Level: \( 2 \)
Weight: \( 0 \)
Character: 2.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 20.1399721518 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+0.274805076\) \(a_{4}=+0.500000000\) \(a_{5}=-0.670981683\)
\(a_{6}=+0.194316533\) \(a_{7}=-0.490917095\) \(a_{8}=+0.353553391\) \(a_{9}=-0.924482170\) \(a_{10}=-0.474455698\)
\(a_{11}=-1.075400973\) \(a_{12}=+0.137402538\) \(a_{13}=+1.445375626\) \(a_{14}=-0.347130807\) \(a_{15}=-0.184389172\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.460914116\) \(a_{18}=-0.653707612\) \(a_{19}=-1.208692055\) \(a_{20}=-0.335490841\)
\(a_{21}=-0.134906510\) \(a_{22}=-0.760423320\) \(a_{23}=-0.534246278\) \(a_{24}=+0.097158266\) \(a_{25}=-0.549783581\)
\(a_{26}=+1.022034906\) \(a_{27}=-0.528857469\) \(a_{28}=-0.245458548\) \(a_{29}=-0.498472450\) \(a_{30}=-0.130382834\)
\(a_{31}=+1.109585032\) \(a_{32}=+0.176776695\) \(a_{33}=-0.295525646\) \(a_{34}=-1.033022279\) \(a_{35}=+0.329396378\)
\(a_{36}=-0.462241085\) \(a_{37}=+1.669984863\) \(a_{38}=-0.854674349\) \(a_{39}=+0.397196559\) \(a_{40}=-0.237227849\)
\(a_{41}=-0.633778918\) \(a_{42}=-0.095393308\) \(a_{43}=+0.730653633\) \(a_{44}=-0.537700487\) \(a_{45}=+0.620310602\)
\(a_{46}=-0.377769166\) \(a_{47}=+0.646947751\) \(a_{48}=+0.068701269\) \(a_{49}=-0.759000406\) \(a_{50}=-0.388755699\)
\(a_{51}=-0.401466615\) \(a_{52}=+0.722687813\) \(a_{53}=+0.612066455\) \(a_{54}=-0.373958703\) \(a_{55}=+0.721574354\)
\(a_{56}=-0.173565404\) \(a_{57}=-0.332154712\) \(a_{58}=-0.352473250\) \(a_{59}=-0.886590081\) \(a_{60}=-0.092194586\)
\(a_{61}=+0.717328919\) \(a_{62}=+0.784595101\) \(a_{63}=+0.453844101\) \(a_{64}=+0.125000000\) \(a_{65}=-0.969820570\)
\(a_{66}=-0.208968188\) \(a_{67}=+0.340348079\) \(a_{68}=-0.730457058\) \(a_{69}=-0.146813589\) \(a_{70}=+0.232918413\)
\(a_{71}=+0.916753169\) \(a_{72}=-0.326853806\) \(a_{73}=-0.579941877\) \(a_{74}=+1.180857621\) \(a_{75}=-0.151083319\)
\(a_{76}=-0.604346028\) \(a_{77}=+0.527932721\) \(a_{78}=+0.280860380\) \(a_{79}=-1.575599519\) \(a_{80}=-0.167745421\)
\(a_{81}=+0.779149453\) \(a_{82}=-0.448149370\) \(a_{83}=+0.417033377\) \(a_{84}=-0.067453255\) \(a_{85}=+0.980246612\)
\(a_{86}=+0.516650138\) \(a_{87}=-0.136982760\) \(a_{88}=-0.380211660\) \(a_{89}=-1.249532419\) \(a_{90}=+0.438625833\)
\(a_{91}=-0.709559603\) \(a_{92}=-0.267123139\) \(a_{93}=+0.304919599\) \(a_{94}=+0.457461142\) \(a_{95}=+0.811010229\)
\(a_{96}=+0.048579133\) \(a_{97}=+0.137667158\) \(a_{98}=-0.536694334\) \(a_{99}=+0.994189025\) \(a_{100}=-0.274891791\)

Showing 100 of 1228 available coefficients

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