Properties

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

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Maass form invariants

Level: \( 13 \)
Weight: \( 0 \)
Character: 13.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 2.81634482766 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.355506567\) \(a_{3}=+0.718720579\) \(a_{4}=-0.873615081\) \(a_{5}=+1.803932179\)
\(a_{6}=+0.255509886\) \(a_{7}=-0.666795368\) \(a_{8}=-0.666082466\) \(a_{9}=-0.483440729\) \(a_{10}=+0.641309737\)
\(a_{11}=+0.544662955\) \(a_{12}=-0.627885137\) \(a_{13}=-0.277350098\) \(a_{14}=-0.237050132\) \(a_{15}=+1.296523181\)
\(a_{16}=+0.636818390\) \(a_{17}=+0.500603108\) \(a_{18}=-0.171866354\) \(a_{19}=-0.363132435\) \(a_{20}=-1.575942356\)
\(a_{21}=-0.479239553\) \(a_{22}=+0.193631257\) \(a_{23}=-0.521462138\) \(a_{24}=-0.478727176\) \(a_{25}=+2.254171306\)
\(a_{26}=-0.098599781\) \(a_{27}=-1.066179380\) \(a_{28}=+0.582522489\) \(a_{29}=+0.155711605\) \(a_{30}=+0.460922505\)
\(a_{31}=-0.417081253\) \(a_{32}=+0.892475585\) \(a_{33}=+0.391460475\) \(a_{34}=+0.177967692\) \(a_{35}=-1.202853622\)
\(a_{36}=+0.422341111\) \(a_{37}=-0.634149539\) \(a_{38}=-0.129095966\) \(a_{39}=-0.199337223\) \(a_{40}=-1.201567594\)
\(a_{41}=+1.580956007\) \(a_{42}=-0.170372809\) \(a_{43}=+0.428041027\) \(a_{44}=-0.475825771\) \(a_{45}=-0.872094287\)
\(a_{46}=-0.185383215\) \(a_{47}=-0.297141409\) \(a_{48}=+0.457694482\) \(a_{49}=-0.555383937\) \(a_{50}=+0.801372703\)
\(a_{51}=+0.359793756\) \(a_{52}=+0.242297228\) \(a_{53}=+1.158425097\) \(a_{54}=-0.379033772\) \(a_{55}=+0.982535031\)
\(a_{56}=+0.444140703\) \(a_{57}=-0.260990754\) \(a_{58}=+0.055356498\) \(a_{59}=-1.461178028\) \(a_{60}=-1.132662203\)
\(a_{61}=+1.338073757\) \(a_{62}=-0.148275125\) \(a_{63}=+0.322356039\) \(a_{64}=-0.319537458\) \(a_{65}=-0.500320767\)
\(a_{66}=+0.139166770\) \(a_{67}=-0.522530196\) \(a_{68}=-0.437334424\) \(a_{69}=-0.374785570\) \(a_{70}=-0.427622362\)
\(a_{71}=-0.350101997\) \(a_{72}=+0.322011393\) \(a_{73}=+0.243650643\) \(a_{74}=-0.225444326\) \(a_{75}=+1.620119307\)
\(a_{76}=+0.317237972\) \(a_{77}=-0.363178736\) \(a_{78}=-0.070865692\) \(a_{79}=-0.451415969\) \(a_{80}=+1.148777185\)
\(a_{81}=-0.282844333\) \(a_{82}=+0.562040243\) \(a_{83}=-0.773153280\) \(a_{84}=+0.418670901\) \(a_{85}=+0.903054055\)
\(a_{86}=+0.152171396\) \(a_{87}=+0.111913135\) \(a_{88}=-0.362790444\) \(a_{89}=-0.202562088\) \(a_{90}=-0.310035246\)
\(a_{91}=+0.184935761\) \(a_{92}=+0.455557188\) \(a_{93}=-0.299764880\) \(a_{94}=-0.105635722\) \(a_{95}=-0.655066285\)
\(a_{96}=+0.641440570\) \(a_{97}=-0.677216597\) \(a_{98}=-0.197442637\) \(a_{99}=-0.263312256\) \(a_{100}=-1.969278047\)

Showing 100 of 546 available coefficients

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