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: \( 2.20427188131 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=+0.184413699\) \(a_{4}=+0.000000000\) \(a_{5}=+0.447213595\)
\(a_{6}=+0.000000000\) \(a_{7}=+1.254055520\) \(a_{8}=+0.000000000\) \(a_{9}=-0.965991588\) \(a_{10}=+0.000000000\)
\(a_{11}=+0.381928270\) \(a_{12}=+0.000000000\) \(a_{13}=-1.551528577\) \(a_{14}=+0.000000000\) \(a_{15}=+0.082472313\)
\(a_{16}=+0.000000000\) \(a_{17}=+1.261472150\) \(a_{18}=+0.000000000\) \(a_{19}=-0.297947250\) \(a_{20}=+0.000000000\)
\(a_{21}=+0.231265017\) \(a_{22}=+0.000000000\) \(a_{23}=+0.856942586\) \(a_{24}=+0.000000000\) \(a_{25}=+0.200000000\)
\(a_{26}=+0.000000000\) \(a_{27}=-0.362555780\) \(a_{28}=+0.000000000\) \(a_{29}=-0.361980306\) \(a_{30}=+0.000000000\)
\(a_{31}=-1.595334733\) \(a_{32}=+0.000000000\) \(a_{33}=+0.070432805\) \(a_{34}=+0.000000000\) \(a_{35}=+0.560830678\)
\(a_{36}=+0.000000000\) \(a_{37}=-0.438725834\) \(a_{38}=+0.000000000\) \(a_{39}=-0.286123123\) \(a_{40}=+0.000000000\)
\(a_{41}=+0.610892710\) \(a_{42}=+0.000000000\) \(a_{43}=+1.203791195\) \(a_{44}=+0.000000000\) \(a_{45}=-0.432004569\)
\(a_{46}=+0.000000000\) \(a_{47}=+0.865748971\) \(a_{48}=+0.000000000\) \(a_{49}=+0.572655256\) \(a_{50}=+0.000000000\)
\(a_{51}=+0.232632735\) \(a_{52}=+0.000000000\) \(a_{53}=-1.668313792\) \(a_{54}=+0.000000000\) \(a_{55}=+0.170803515\)
\(a_{56}=+0.000000000\) \(a_{57}=-0.054945590\) \(a_{58}=+0.000000000\) \(a_{59}=-0.381685444\) \(a_{60}=+0.000000000\)
\(a_{61}=+0.392339536\) \(a_{62}=+0.000000000\) \(a_{63}=-1.211407066\) \(a_{64}=+0.000000000\) \(a_{65}=-0.693864802\)
\(a_{66}=+0.000000000\) \(a_{67}=+0.031063365\) \(a_{68}=+0.000000000\) \(a_{69}=+0.158032503\) \(a_{70}=+0.000000000\)
\(a_{71}=+0.599524846\) \(a_{72}=+0.000000000\) \(a_{73}=+0.409562598\) \(a_{74}=+0.000000000\) \(a_{75}=+0.036882349\)
\(a_{76}=+0.000000000\) \(a_{77}=+0.478960446\) \(a_{78}=+0.000000000\) \(a_{79}=-0.182991104\) \(a_{80}=+0.000000000\)
\(a_{81}=+0.899126649\) \(a_{82}=+0.000000000\) \(a_{83}=+0.478008364\) \(a_{84}=+0.000000000\) \(a_{85}=+0.564206649\)
\(a_{86}=+0.000000000\) \(a_{87}=-0.066715640\) \(a_{88}=+0.000000000\) \(a_{89}=+0.690515029\) \(a_{90}=+0.000000000\)
\(a_{91}=-1.945702855\) \(a_{92}=+0.000000000\) \(a_{93}=-0.294203840\) \(a_{94}=+0.000000000\) \(a_{95}=-0.133243086\)
\(a_{96}=+0.000000000\) \(a_{97}=-0.630069364\) \(a_{98}=+0.000000000\) \(a_{99}=-0.368943380\) \(a_{100}=+0.000000000\)

Showing 100 of 2000 available coefficients

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