Properties

Level $53$
Weight $0$
Character 53.1
Symmetry even
Fricke sign $-1$

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Maass form invariants

Level: \( 53 \)
Weight: \( 0 \)
Character: 53.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 3.81318882937 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.588412411\) \(a_{3}=+0.999116765\) \(a_{4}=-0.653770834\) \(a_{5}=+0.230891178\)
\(a_{6}=+0.587892705\) \(a_{7}=-1.144032507\) \(a_{8}=-0.973099284\) \(a_{9}=-0.001765690\) \(a_{10}=+0.135859235\)
\(a_{11}=-1.459824412\) \(a_{12}=-0.653193401\) \(a_{13}=+0.136980103\) \(a_{14}=-0.673162926\) \(a_{15}=+0.230687247\)
\(a_{16}=+0.081187138\) \(a_{17}=+0.600099432\) \(a_{18}=-0.001038954\) \(a_{19}=+0.330473075\) \(a_{20}=-0.150949918\)
\(a_{21}=-1.143022057\) \(a_{22}=-0.858978802\) \(a_{23}=-0.085397973\) \(a_{24}=-0.972239809\) \(a_{25}=-0.946689264\)
\(a_{26}=+0.080600793\) \(a_{27}=-1.000880895\) \(a_{28}=+0.747935087\) \(a_{29}=-0.374127306\) \(a_{30}=+0.135739239\)
\(a_{31}=+1.355527402\) \(a_{32}=+1.020870804\) \(a_{33}=-1.458535044\) \(a_{34}=+0.353105954\) \(a_{35}=-0.264147014\)
\(a_{36}=+0.001154357\) \(a_{37}=-1.129634068\) \(a_{38}=+0.194454459\) \(a_{39}=+0.136859117\) \(a_{40}=-0.224680040\)
\(a_{41}=+0.619468859\) \(a_{42}=-0.672568365\) \(a_{43}=+0.349426221\) \(a_{44}=+0.954390624\) \(a_{45}=-0.000407682\)
\(a_{46}=-0.050249227\) \(a_{47}=+0.501841450\) \(a_{48}=+0.081115431\) \(a_{49}=+0.308810377\) \(a_{50}=-0.557043712\)
\(a_{51}=+0.599569403\) \(a_{52}=-0.089553596\) \(a_{53}=+0.137360564\) \(a_{54}=-0.588930741\) \(a_{55}=-0.337060579\)
\(a_{56}=+1.113257213\) \(a_{57}=+0.330181189\) \(a_{58}=-0.220141150\) \(a_{59}=+0.299835689\) \(a_{60}=-0.150816594\)
\(a_{61}=-1.511547165\) \(a_{62}=+0.797609147\) \(a_{63}=+0.002020007\) \(a_{64}=+0.519505913\) \(a_{65}=+0.031627497\)
\(a_{66}=-0.858220122\) \(a_{67}=-1.875318396\) \(a_{68}=-0.392327507\) \(a_{69}=-0.085322547\) \(a_{70}=-0.155427381\)
\(a_{71}=-0.355718361\) \(a_{72}=+0.001718192\) \(a_{73}=-0.003390153\) \(a_{74}=-0.664690706\) \(a_{75}=-0.945853115\)
\(a_{76}=-0.216053658\) \(a_{77}=+1.670086582\) \(a_{78}=+0.080529603\) \(a_{79}=+0.819738289\) \(a_{80}=+0.018745394\)
\(a_{81}=-0.998231192\) \(a_{82}=+0.364503165\) \(a_{83}=-1.366153974\) \(a_{84}=+0.747274484\) \(a_{85}=+0.138557665\)
\(a_{86}=+0.205606725\) \(a_{87}=-0.373796864\) \(a_{88}=+1.420554090\) \(a_{89}=+1.836928519\) \(a_{90}=-0.000239885\)
\(a_{91}=-0.156709690\) \(a_{92}=+0.055830704\) \(a_{93}=+1.354330153\) \(a_{94}=+0.295289738\) \(a_{95}=+0.076303318\)
\(a_{96}=+1.019969135\) \(a_{97}=-1.064148594\) \(a_{98}=+0.181707858\) \(a_{99}=+0.002577597\) \(a_{100}=+0.618917830\)

Showing 100 of 546 available coefficients

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