Properties

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

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Maass form invariants

Level: \( 13 \)
Weight: \( 0 \)
Character: 13.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 5.59109262478 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.413117081\) \(a_{3}=+0.682183673\) \(a_{4}=+0.996899886\) \(a_{5}=+0.253740863\)
\(a_{6}=-0.964005401\) \(a_{7}=+0.103408148\) \(a_{8}=+0.004380824\) \(a_{9}=-0.534625437\) \(a_{10}=-0.358565548\)
\(a_{11}=-0.971409961\) \(a_{12}=+0.680068826\) \(a_{13}=-0.277350098\) \(a_{14}=-0.146127820\) \(a_{15}=+0.173097874\)
\(a_{16}=-1.003090503\) \(a_{17}=-0.354446473\) \(a_{18}=+0.755488337\) \(a_{19}=-1.025658108\) \(a_{20}=+0.252954237\)
\(a_{21}=+0.070543350\) \(a_{22}=+1.372716008\) \(a_{23}=+0.698335254\) \(a_{24}=+0.002988527\) \(a_{25}=-0.935615574\)
\(a_{26}=+0.391928161\) \(a_{27}=-1.046896417\) \(a_{28}=+0.103087571\) \(a_{29}=-1.361222587\) \(a_{30}=-0.244607562\)
\(a_{31}=+0.055240592\) \(a_{32}=+1.413103500\) \(a_{33}=-0.662680015\) \(a_{34}=+0.500874365\) \(a_{35}=+0.026238873\)
\(a_{36}=-0.532968037\) \(a_{37}=+0.389560218\) \(a_{38}=+1.449374992\) \(a_{39}=-0.189203708\) \(a_{40}=+0.001111593\)
\(a_{41}=+1.928982180\) \(a_{42}=-0.099686010\) \(a_{43}=-1.605451004\) \(a_{44}=-0.968398487\) \(a_{45}=-0.135656321\)
\(a_{46}=-0.986829457\) \(a_{47}=-0.000198006\) \(a_{48}=-0.684292003\) \(a_{49}=-0.989306755\) \(a_{50}=+1.322134350\)
\(a_{51}=-0.241797597\) \(a_{52}=-0.276490281\) \(a_{53}=+1.438274726\) \(a_{54}=+1.479387209\) \(a_{55}=-0.246486402\)
\(a_{56}=+0.000453013\) \(a_{57}=-0.699687215\) \(a_{58}=+1.923566890\) \(a_{59}=-1.538558301\) \(a_{60}=+0.172561251\)
\(a_{61}=-0.202531490\) \(a_{62}=-0.078061424\) \(a_{63}=-0.055284626\) \(a_{64}=-0.993790191\) \(a_{65}=-0.070375053\)
\(a_{66}=+0.936444449\) \(a_{67}=-0.334225981\) \(a_{68}=-0.353347648\) \(a_{69}=+0.476392908\) \(a_{70}=-0.037078599\)
\(a_{71}=+1.425396627\) \(a_{72}=-0.002342101\) \(a_{73}=-0.112273055\) \(a_{74}=-0.550494199\) \(a_{75}=-0.638261669\)
\(a_{76}=-1.022478451\) \(a_{77}=-0.100451707\) \(a_{78}=+0.267366997\) \(a_{79}=+0.812176724\) \(a_{80}=-0.254525049\)
\(a_{81}=-0.179550209\) \(a_{82}=-2.725877669\) \(a_{83}=+1.337367643\) \(a_{84}=+0.070324622\) \(a_{85}=-0.089937571\)
\(a_{86}=+2.268690228\) \(a_{87}=-0.928603816\) \(a_{88}=-0.004255534\) \(a_{89}=+0.606855586\) \(a_{90}=+0.191698269\)
\(a_{91}=-0.028680260\) \(a_{92}=+0.696170335\) \(a_{93}=+0.037684230\) \(a_{94}=+0.000279800\) \(a_{95}=-0.260251373\)
\(a_{96}=+0.963996136\) \(a_{97}=-0.535590486\) \(a_{98}=+1.398006275\) \(a_{99}=+0.519340474\) \(a_{100}=-0.932715059\)

Showing 100 of 1000 available coefficients

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