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: \( 15.3141965842 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-0.052709328\) \(a_{4}=+0.500000000\) \(a_{5}=-1.418216499\)
\(a_{6}=-0.037271123\) \(a_{7}=+0.266660233\) \(a_{8}=+0.353553391\) \(a_{9}=-0.997221727\) \(a_{10}=-1.002830503\)
\(a_{11}=-0.866528144\) \(a_{12}=-0.026354664\) \(a_{13}=-1.351964758\) \(a_{14}=+0.188557259\) \(a_{15}=+0.074753239\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.742796919\) \(a_{18}=-0.705142245\) \(a_{19}=+1.761780126\) \(a_{20}=-0.709108249\)
\(a_{21}=-0.014055482\) \(a_{22}=-0.612727927\) \(a_{23}=+0.300245668\) \(a_{24}=-0.018635562\) \(a_{25}=+1.011338037\)
\(a_{26}=-0.955983448\) \(a_{27}=+0.105272215\) \(a_{28}=+0.133330117\) \(a_{29}=-0.570335841\) \(a_{30}=+0.052858522\)
\(a_{31}=+0.710052601\) \(a_{32}=+0.176776695\) \(a_{33}=+0.045674116\) \(a_{34}=-0.525236739\) \(a_{35}=-0.378181942\)
\(a_{36}=-0.498610863\) \(a_{37}=+0.388420849\) \(a_{38}=+1.245766674\) \(a_{39}=+0.071261154\) \(a_{40}=-0.501415252\)
\(a_{41}=-0.427646811\) \(a_{42}=-0.009938726\) \(a_{43}=-0.490294914\) \(a_{44}=-0.433264072\) \(a_{45}=+1.414276306\)
\(a_{46}=+0.212305748\) \(a_{47}=-0.138044735\) \(a_{48}=-0.013177332\) \(a_{49}=-0.928892320\) \(a_{50}=+0.715123984\)
\(a_{51}=+0.039152326\) \(a_{52}=-0.675982379\) \(a_{53}=-0.380611238\) \(a_{54}=+0.074438697\) \(a_{55}=+1.228924510\)
\(a_{56}=+0.094278630\) \(a_{57}=-0.092862246\) \(a_{58}=-0.403288340\) \(a_{59}=+0.496125848\) \(a_{60}=+0.037376619\)
\(a_{61}=-1.843815599\) \(a_{62}=+0.502083009\) \(a_{63}=-0.265919378\) \(a_{64}=+0.125000000\) \(a_{65}=+1.917378725\)
\(a_{66}=+0.032296477\) \(a_{67}=-0.462358963\) \(a_{68}=-0.371398460\) \(a_{69}=-0.015825747\) \(a_{70}=-0.267415016\)
\(a_{71}=-0.629644011\) \(a_{72}=-0.352571123\) \(a_{73}=+0.557039669\) \(a_{74}=+0.274655016\) \(a_{75}=-0.053306948\)
\(a_{76}=+0.880890063\) \(a_{77}=-0.231068597\) \(a_{78}=+0.050389245\) \(a_{79}=-0.292483606\) \(a_{80}=-0.354554125\)
\(a_{81}=+0.991672899\) \(a_{82}=-0.302391960\) \(a_{83}=-1.570142008\) \(a_{84}=-0.007027741\) \(a_{85}=+1.053446846\)
\(a_{86}=-0.346690858\) \(a_{87}=+0.030062019\) \(a_{88}=-0.306363963\) \(a_{89}=+0.766845806\) \(a_{90}=+1.000044366\)
\(a_{91}=-0.360515238\) \(a_{92}=+0.150122834\) \(a_{93}=-0.037426395\) \(a_{94}=-0.097612368\) \(a_{95}=-2.498585641\)
\(a_{96}=-0.009317781\) \(a_{97}=+1.410698427\) \(a_{98}=-0.656826058\) \(a_{99}=+0.864120692\) \(a_{100}=+0.505669018\)

Showing 100 of 1228 available coefficients

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