Properties

Level $20$
Weight $0$
Character 20.1
Symmetry even
Fricke sign $-1$

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Maass form invariants

Level: \( 20 = 2^{2} \cdot 5 \)
Weight: \( 0 \)
Character: 20.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 3.44478653588 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=-0.533687032\) \(a_{4}=+0.000000000\) \(a_{5}=-0.447213595\)
\(a_{6}=+0.000000000\) \(a_{7}=-0.686652952\) \(a_{8}=+0.000000000\) \(a_{9}=-0.715178152\) \(a_{10}=+0.000000000\)
\(a_{11}=-0.576204708\) \(a_{12}=+0.000000000\) \(a_{13}=+0.448649126\) \(a_{14}=+0.000000000\) \(a_{15}=+0.238672096\)
\(a_{16}=+0.000000000\) \(a_{17}=+1.584354383\) \(a_{18}=+0.000000000\) \(a_{19}=-1.346424219\) \(a_{20}=+0.000000000\)
\(a_{21}=+0.366457776\) \(a_{22}=+0.000000000\) \(a_{23}=-1.845683995\) \(a_{24}=+0.000000000\) \(a_{25}=+0.200000000\)
\(a_{26}=+0.000000000\) \(a_{27}=+0.915368337\) \(a_{28}=+0.000000000\) \(a_{29}=-0.847173752\) \(a_{30}=+0.000000000\)
\(a_{31}=+0.418557066\) \(a_{32}=+0.000000000\) \(a_{33}=+0.307512980\) \(a_{34}=+0.000000000\) \(a_{35}=+0.307080536\)
\(a_{36}=+0.000000000\) \(a_{37}=+1.364971103\) \(a_{38}=+0.000000000\) \(a_{39}=-0.239438220\) \(a_{40}=+0.000000000\)
\(a_{41}=-1.252414868\) \(a_{42}=+0.000000000\) \(a_{43}=+0.697685102\) \(a_{44}=+0.000000000\) \(a_{45}=+0.319837393\)
\(a_{46}=+0.000000000\) \(a_{47}=-1.064688738\) \(a_{48}=+0.000000000\) \(a_{49}=-0.528507722\) \(a_{50}=+0.000000000\)
\(a_{51}=-0.845549389\) \(a_{52}=+0.000000000\) \(a_{53}=-0.247029064\) \(a_{54}=+0.000000000\) \(a_{55}=+0.257686575\)
\(a_{56}=+0.000000000\) \(a_{57}=+0.718569146\) \(a_{58}=+0.000000000\) \(a_{59}=-0.525701141\) \(a_{60}=+0.000000000\)
\(a_{61}=+1.551256500\) \(a_{62}=+0.000000000\) \(a_{63}=+0.491079162\) \(a_{64}=+0.000000000\) \(a_{65}=-0.200641963\)
\(a_{66}=+0.000000000\) \(a_{67}=+0.219991543\) \(a_{68}=+0.000000000\) \(a_{69}=+0.985017612\) \(a_{70}=+0.000000000\)
\(a_{71}=-0.005883170\) \(a_{72}=+0.000000000\) \(a_{73}=-1.655444718\) \(a_{74}=+0.000000000\) \(a_{75}=-0.106737404\)
\(a_{76}=+0.000000000\) \(a_{77}=+0.395652667\) \(a_{78}=+0.000000000\) \(a_{79}=-0.412999451\) \(a_{80}=+0.000000000\)
\(a_{81}=+0.226657954\) \(a_{82}=+0.000000000\) \(a_{83}=-0.631969597\) \(a_{84}=+0.000000000\) \(a_{85}=-0.708544852\)
\(a_{86}=+0.000000000\) \(a_{87}=+0.452125612\) \(a_{88}=+0.000000000\) \(a_{89}=-0.488732828\) \(a_{90}=+0.000000000\)
\(a_{91}=-0.308065008\) \(a_{92}=+0.000000000\) \(a_{93}=-0.223379723\) \(a_{94}=+0.000000000\) \(a_{95}=+0.602141287\)
\(a_{96}=+0.000000000\) \(a_{97}=-0.517981638\) \(a_{98}=+0.000000000\) \(a_{99}=+0.412090438\) \(a_{100}=+0.000000000\)

Showing 100 of 2000 available coefficients

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