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: \( 4.89717909208 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.737361885\) \(a_{3}=-1.209902547\) \(a_{4}=-0.456297450\) \(a_{5}=+1.373987219\)
\(a_{6}=+0.892136024\) \(a_{7}=-1.231117372\) \(a_{8}=+1.073818233\) \(a_{9}=+0.463864174\) \(a_{10}=-1.013125807\)
\(a_{11}=+0.911441228\) \(a_{12}=+0.552075447\) \(a_{13}=+0.277350098\) \(a_{14}=+0.907779026\) \(a_{15}=-1.662390637\)
\(a_{16}=-0.335495187\) \(a_{17}=+1.623063456\) \(a_{18}=-0.342035762\) \(a_{19}=-0.888437758\) \(a_{20}=-0.626946864\)
\(a_{21}=+1.489532044\) \(a_{22}=-0.672062023\) \(a_{23}=+0.114996645\) \(a_{24}=-1.299215416\) \(a_{25}=+0.887840879\)
\(a_{26}=-0.204507391\) \(a_{27}=+0.648672101\) \(a_{28}=+0.561755717\) \(a_{29}=+0.470461741\) \(a_{30}=+1.225783494\)
\(a_{31}=+0.420787370\) \(a_{32}=-0.826436870\) \(a_{33}=-1.102755064\) \(a_{34}=-1.196785130\) \(a_{35}=-1.691539534\)
\(a_{36}=-0.211660040\) \(a_{37}=+0.739491592\) \(a_{38}=+0.655100140\) \(a_{39}=-0.335566590\) \(a_{40}=+1.475412529\)
\(a_{41}=+0.585314256\) \(a_{42}=-1.098324156\) \(a_{43}=+0.551214920\) \(a_{44}=-0.415888308\) \(a_{45}=+0.637343447\)
\(a_{46}=-0.084794143\) \(a_{47}=+0.935785798\) \(a_{48}=+0.405916482\) \(a_{49}=+0.515649983\) \(a_{50}=-0.654660024\)
\(a_{51}=-1.963748610\) \(a_{52}=-0.126554143\) \(a_{53}=+0.570329561\) \(a_{54}=-0.478306084\) \(a_{55}=+1.252308599\)
\(a_{56}=-1.321996281\) \(a_{57}=+1.074923107\) \(a_{58}=-0.346900557\) \(a_{59}=-0.850609367\) \(a_{60}=+0.758544608\)
\(a_{61}=-0.930717491\) \(a_{62}=-0.310272569\) \(a_{63}=-0.571071243\) \(a_{64}=+0.944878236\) \(a_{65}=+0.381075490\)
\(a_{66}=+0.813129553\) \(a_{67}=-1.208402188\) \(a_{68}=-0.740599716\) \(a_{69}=-0.139134733\) \(a_{70}=+1.247276780\)
\(a_{71}=+1.524605590\) \(a_{72}=+0.498105808\) \(a_{73}=+0.980445513\) \(a_{74}=-0.545272915\) \(a_{75}=-1.074200941\)
\(a_{76}=+0.405391883\) \(a_{77}=-1.122091129\) \(a_{78}=+0.247434014\) \(a_{79}=+0.712122950\) \(a_{80}=-0.460966099\)
\(a_{81}=-1.248694202\) \(a_{82}=-0.431588423\) \(a_{83}=+0.511526615\) \(a_{84}=-0.679669673\) \(a_{85}=+2.230068444\)
\(a_{86}=-0.406444873\) \(a_{87}=-0.569212860\) \(a_{88}=+0.978722210\) \(a_{89}=-0.703935786\) \(a_{90}=-0.469952766\)
\(a_{91}=-0.341450524\) \(a_{92}=-0.052472676\) \(a_{93}=-0.509111712\) \(a_{94}=-0.690012780\) \(a_{95}=-1.220702125\)
\(a_{96}=+0.999908074\) \(a_{97}=+0.710800308\) \(a_{98}=-0.380220643\) \(a_{99}=+0.422784933\) \(a_{100}=-0.405119529\)

Showing 100 of 546 available coefficients

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