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: \( 22.0890454668 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-1.160405712\) \(a_{4}=+0.500000000\) \(a_{5}=+1.627801546\)
\(a_{6}=+0.820530748\) \(a_{7}=-1.268072183\) \(a_{8}=-0.353553391\) \(a_{9}=+0.346541417\) \(a_{10}=-1.151029512\)
\(a_{11}=-0.749343856\) \(a_{12}=-0.580202856\) \(a_{13}=+0.320358354\) \(a_{14}=+0.896662440\) \(a_{15}=-1.888910213\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.577219228\) \(a_{18}=-0.245041786\) \(a_{19}=-0.008501526\) \(a_{20}=+0.813900773\)
\(a_{21}=+1.471478205\) \(a_{22}=+0.529866122\) \(a_{23}=+0.339032492\) \(a_{24}=+0.410265374\) \(a_{25}=+1.649737875\)
\(a_{26}=-0.226527564\) \(a_{27}=+0.758277072\) \(a_{28}=-0.634036091\) \(a_{29}=+0.019990783\) \(a_{30}=+1.335661221\)
\(a_{31}=-0.724552297\) \(a_{32}=-0.176776695\) \(a_{33}=+0.869542891\) \(a_{34}=+0.408155630\) \(a_{35}=-2.064169860\)
\(a_{36}=+0.173270709\) \(a_{37}=+1.788758459\) \(a_{38}=+0.006011487\) \(a_{39}=-0.371745664\) \(a_{40}=-0.575514756\)
\(a_{41}=-0.007324855\) \(a_{42}=-1.040492217\) \(a_{43}=+1.687109674\) \(a_{44}=-0.374671928\) \(a_{45}=+0.564100655\)
\(a_{46}=-0.239732174\) \(a_{47}=-0.470629902\) \(a_{48}=-0.290101428\) \(a_{49}=+0.608007061\) \(a_{50}=-1.166540838\)
\(a_{51}=+0.669808489\) \(a_{52}=+0.160179177\) \(a_{53}=+1.291905372\) \(a_{54}=-0.536182860\) \(a_{55}=-1.219783088\)
\(a_{56}=+0.448331220\) \(a_{57}=+0.009865219\) \(a_{58}=-0.014135618\) \(a_{59}=+0.094149296\) \(a_{60}=-0.944455106\)
\(a_{61}=+1.093902666\) \(a_{62}=+0.512335843\) \(a_{63}=-0.439439531\) \(a_{64}=+0.125000000\) \(a_{65}=+0.521479824\)
\(a_{66}=-0.614859675\) \(a_{67}=-0.946272090\) \(a_{68}=-0.288609614\) \(a_{69}=-0.393415241\) \(a_{70}=+1.459588506\)
\(a_{71}=+0.604019745\) \(a_{72}=-0.122520893\) \(a_{73}=+1.434145013\) \(a_{74}=-1.264843236\) \(a_{75}=-1.914365253\)
\(a_{76}=-0.004250763\) \(a_{77}=+0.950222100\) \(a_{78}=+0.262863880\) \(a_{79}=+0.011519967\) \(a_{80}=+0.406950387\)
\(a_{81}=-1.226450463\) \(a_{82}=+0.005179455\) \(a_{83}=+1.687786347\) \(a_{84}=+0.735739102\) \(a_{85}=-0.939598352\)
\(a_{86}=-1.192966691\) \(a_{87}=-0.023197419\) \(a_{88}=+0.264933061\) \(a_{89}=+0.274557263\) \(a_{90}=-0.398879398\)
\(a_{91}=-0.406237517\) \(a_{92}=+0.169516246\) \(a_{93}=+0.840774625\) \(a_{94}=+0.332785595\) \(a_{95}=-0.013838797\)
\(a_{96}=+0.205132687\) \(a_{97}=-0.281586785\) \(a_{98}=-0.429925916\) \(a_{99}=-0.259678682\) \(a_{100}=+0.824868937\)

Showing 100 of 1228 available coefficients

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