Properties

Level $13$
Weight $0$
Character 13.1
Symmetry odd
Fricke sign $+1$

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 13 \)
Weight: \( 0 \)
Character: 13.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 7.75262012727 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.525956051\) \(a_{3}=+1.490856615\) \(a_{4}=-0.723370233\) \(a_{5}=-0.121759635\)
\(a_{6}=-0.784125058\) \(a_{7}=-0.439516708\) \(a_{8}=+0.906417002\) \(a_{9}=+1.222653447\) \(a_{10}=+0.064040217\)
\(a_{11}=-0.558615968\) \(a_{12}=-1.078441296\) \(a_{13}=-0.277350098\) \(a_{14}=+0.231166472\) \(a_{15}=-0.181526157\)
\(a_{16}=+0.246634726\) \(a_{17}=-0.702958138\) \(a_{18}=-0.643061978\) \(a_{19}=-1.081968840\) \(a_{20}=+0.088077295\)
\(a_{21}=-0.655256392\) \(a_{22}=+0.293807448\) \(a_{23}=-1.527878084\) \(a_{24}=+1.351337783\) \(a_{25}=-0.985174591\)
\(a_{26}=+0.145873962\) \(a_{27}=+0.331944364\) \(a_{28}=+0.317933303\) \(a_{29}=-0.433213600\) \(a_{30}=+0.095474781\)
\(a_{31}=+1.504466016\) \(a_{32}=-1.036136028\) \(a_{33}=-0.832816311\) \(a_{34}=+0.369725086\) \(a_{35}=+0.053515394\)
\(a_{36}=-0.884431108\) \(a_{37}=-1.014910377\) \(a_{38}=+0.569068058\) \(a_{39}=-0.413489228\) \(a_{40}=-0.110365003\)
\(a_{41}=+0.473170884\) \(a_{42}=+0.344636064\) \(a_{43}=+1.161020580\) \(a_{44}=+0.404086163\) \(a_{45}=-0.148869837\)
\(a_{46}=+0.803596723\) \(a_{47}=-0.906512502\) \(a_{48}=+0.367697013\) \(a_{49}=-0.806825063\) \(a_{50}=+0.518158537\)
\(a_{51}=-1.048009790\) \(a_{52}=+0.200626805\) \(a_{53}=+0.013076017\) \(a_{54}=-0.174588147\) \(a_{55}=+0.068016876\)
\(a_{56}=-0.398385417\) \(a_{57}=-1.613060403\) \(a_{58}=+0.227851314\) \(a_{59}=+1.338833114\) \(a_{60}=+0.131310619\)
\(a_{61}=+1.644198681\) \(a_{62}=-0.791283004\) \(a_{63}=-0.537376618\) \(a_{64}=+0.298327287\) \(a_{65}=+0.033770047\)
\(a_{66}=+0.438024778\) \(a_{67}=-1.078504656\) \(a_{68}=+0.508498992\) \(a_{69}=-2.277847149\) \(a_{70}=-0.028146745\)
\(a_{71}=+1.653520695\) \(a_{72}=+1.108233871\) \(a_{73}=+1.227906188\) \(a_{74}=+0.533798254\) \(a_{75}=-1.468754056\)
\(a_{76}=+0.782664052\) \(a_{77}=+0.245521051\) \(a_{78}=+0.217477162\) \(a_{79}=-1.250072546\) \(a_{80}=-0.030030154\)
\(a_{81}=-0.727771996\) \(a_{82}=-0.248867089\) \(a_{83}=-1.239815737\) \(a_{84}=+0.473992969\) \(a_{85}=+0.085591926\)
\(a_{86}=-0.610645799\) \(a_{87}=-0.645859362\) \(a_{88}=-0.506339011\) \(a_{89}=+0.070002035\) \(a_{90}=+0.078298992\)
\(a_{91}=+0.121900002\) \(a_{92}=+1.105221525\) \(a_{93}=+2.242943111\) \(a_{94}=+0.476785735\) \(a_{95}=+0.131740131\)
\(a_{96}=-1.544730252\) \(a_{97}=+1.147039238\) \(a_{98}=+0.424354524\) \(a_{99}=-0.682993738\) \(a_{100}=+0.712645973\)

Showing 100 of 546 available coefficients

Rows: Cols: