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: \( 3.92397086259 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=+1.944787286\) \(a_{4}=+0.000000000\) \(a_{5}=+0.447213595\)
\(a_{6}=+0.000000000\) \(a_{7}=-0.022282455\) \(a_{8}=+0.000000000\) \(a_{9}=+2.782197589\) \(a_{10}=+0.000000000\)
\(a_{11}=-0.692388671\) \(a_{12}=+0.000000000\) \(a_{13}=-0.576035551\) \(a_{14}=+0.000000000\) \(a_{15}=+0.869735315\)
\(a_{16}=+0.000000000\) \(a_{17}=-0.561905254\) \(a_{18}=+0.000000000\) \(a_{19}=+0.041982544\) \(a_{20}=+0.000000000\)
\(a_{21}=-0.043334635\) \(a_{22}=+0.000000000\) \(a_{23}=-0.979845735\) \(a_{24}=+0.000000000\) \(a_{25}=+0.200000000\)
\(a_{26}=+0.000000000\) \(a_{27}=+3.465995213\) \(a_{28}=+0.000000000\) \(a_{29}=-0.615422076\) \(a_{30}=+0.000000000\)
\(a_{31}=-0.588570120\) \(a_{32}=+0.000000000\) \(a_{33}=-1.346548684\) \(a_{34}=+0.000000000\) \(a_{35}=-0.009965017\)
\(a_{36}=+0.000000000\) \(a_{37}=-0.830699355\) \(a_{38}=+0.000000000\) \(a_{39}=-1.120266616\) \(a_{40}=+0.000000000\)
\(a_{41}=+1.117321988\) \(a_{42}=+0.000000000\) \(a_{43}=+0.227299607\) \(a_{44}=+0.000000000\) \(a_{45}=+1.244236586\)
\(a_{46}=+0.000000000\) \(a_{47}=+1.088559640\) \(a_{48}=+0.000000000\) \(a_{49}=-0.999503491\) \(a_{50}=+0.000000000\)
\(a_{51}=-1.092786195\) \(a_{52}=+0.000000000\) \(a_{53}=+1.094735687\) \(a_{54}=+0.000000000\) \(a_{55}=-0.309645613\)
\(a_{56}=+0.000000000\) \(a_{57}=+0.081647081\) \(a_{58}=+0.000000000\) \(a_{59}=+1.436186201\) \(a_{60}=+0.000000000\)
\(a_{61}=-1.214718759\) \(a_{62}=+0.000000000\) \(a_{63}=-0.061994193\) \(a_{64}=+0.000000000\) \(a_{65}=-0.257610930\)
\(a_{66}=+0.000000000\) \(a_{67}=+1.028981549\) \(a_{68}=+0.000000000\) \(a_{69}=-1.905591522\) \(a_{70}=+0.000000000\)
\(a_{71}=-0.732681901\) \(a_{72}=+0.000000000\) \(a_{73}=-1.602816197\) \(a_{74}=+0.000000000\) \(a_{75}=+0.388957451\)
\(a_{76}=+0.000000000\) \(a_{77}=+0.015428117\) \(a_{78}=+0.000000000\) \(a_{79}=+0.611782793\) \(a_{80}=+0.000000000\)
\(a_{81}=+3.958425847\) \(a_{82}=+0.000000000\) \(a_{83}=+0.357712484\) \(a_{84}=+0.000000000\) \(a_{85}=-0.251291910\)
\(a_{86}=+0.000000000\) \(a_{87}=-1.196864911\) \(a_{88}=+0.000000000\) \(a_{89}=+0.863795899\) \(a_{90}=+0.000000000\)
\(a_{91}=+0.012835486\) \(a_{92}=+0.000000000\) \(a_{93}=-1.144643687\) \(a_{94}=+0.000000000\) \(a_{95}=+0.018775163\)
\(a_{96}=+0.000000000\) \(a_{97}=+0.878376930\) \(a_{98}=+0.000000000\) \(a_{99}=-1.926362088\) \(a_{100}=+0.000000000\)

Showing 100 of 2000 available coefficients

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