Properties

Level $28$
Weight $0$
Character 28.1
Symmetry even
Fricke sign $-1$

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Maass form invariants

Level: \( 28 = 2^{2} \cdot 7 \)
Weight: \( 0 \)
Character: 28.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 4.40753430907 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=+1.107159594\) \(a_{4}=+0.000000000\) \(a_{5}=-1.339866789\)
\(a_{6}=+0.000000000\) \(a_{7}=-0.377964473\) \(a_{8}=+0.000000000\) \(a_{9}=+0.225802367\) \(a_{10}=+0.000000000\)
\(a_{11}=-1.349136670\) \(a_{12}=+0.000000000\) \(a_{13}=-0.577390842\) \(a_{14}=+0.000000000\) \(a_{15}=-1.483446370\)
\(a_{16}=+0.000000000\) \(a_{17}=+1.096864741\) \(a_{18}=+0.000000000\) \(a_{19}=-1.584784835\) \(a_{20}=+0.000000000\)
\(a_{21}=-0.418466992\) \(a_{22}=+0.000000000\) \(a_{23}=+1.006896496\) \(a_{24}=+0.000000000\) \(a_{25}=+0.795243013\)
\(a_{26}=+0.000000000\) \(a_{27}=-0.857160337\) \(a_{28}=+0.000000000\) \(a_{29}=+0.080094195\) \(a_{30}=+0.000000000\)
\(a_{31}=+1.314754143\) \(a_{32}=+0.000000000\) \(a_{33}=-1.493709608\) \(a_{34}=+0.000000000\) \(a_{35}=+0.506422045\)
\(a_{36}=+0.000000000\) \(a_{37}=-0.111708767\) \(a_{38}=+0.000000000\) \(a_{39}=-0.639263810\) \(a_{40}=+0.000000000\)
\(a_{41}=-1.318238060\) \(a_{42}=+0.000000000\) \(a_{43}=-0.443590522\) \(a_{44}=+0.000000000\) \(a_{45}=-0.302545092\)
\(a_{46}=+0.000000000\) \(a_{47}=+1.228084448\) \(a_{48}=+0.000000000\) \(a_{49}=+0.142857143\) \(a_{50}=+0.000000000\)
\(a_{51}=+1.214404322\) \(a_{52}=+0.000000000\) \(a_{53}=+1.026875206\) \(a_{54}=+0.000000000\) \(a_{55}=+1.807663418\)
\(a_{56}=+0.000000000\) \(a_{57}=-1.754609735\) \(a_{58}=+0.000000000\) \(a_{59}=-0.942911544\) \(a_{60}=+0.000000000\)
\(a_{61}=-0.694370314\) \(a_{62}=+0.000000000\) \(a_{63}=-0.085345272\) \(a_{64}=+0.000000000\) \(a_{65}=+0.773626813\)
\(a_{66}=+0.000000000\) \(a_{67}=-0.710234071\) \(a_{68}=+0.000000000\) \(a_{69}=+1.114795115\) \(a_{70}=+0.000000000\)
\(a_{71}=-1.550240788\) \(a_{72}=+0.000000000\) \(a_{73}=-0.130068622\) \(a_{74}=+0.000000000\) \(a_{75}=+0.880460932\)
\(a_{76}=+0.000000000\) \(a_{77}=+0.509925731\) \(a_{78}=+0.000000000\) \(a_{79}=-1.624904847\) \(a_{80}=+0.000000000\)
\(a_{81}=-1.174815658\) \(a_{82}=+0.000000000\) \(a_{83}=+1.526791331\) \(a_{84}=+0.000000000\) \(a_{85}=-1.469652639\)
\(a_{86}=+0.000000000\) \(a_{87}=+0.088677057\) \(a_{88}=+0.000000000\) \(a_{89}=+0.741712427\) \(a_{90}=+0.000000000\)
\(a_{91}=+0.218233225\) \(a_{92}=+0.000000000\) \(a_{93}=+1.455642663\) \(a_{94}=+0.000000000\) \(a_{95}=+2.123400569\)
\(a_{96}=+0.000000000\) \(a_{97}=-1.564980988\) \(a_{98}=+0.000000000\) \(a_{99}=-0.304638253\) \(a_{100}=+0.000000000\)

Showing 100 of 282 available coefficients

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