Properties

Level $56$
Weight $0$
Character 56.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 56 = 2^{3} \cdot 7 \)
Weight: \( 0 \)
Character: 56.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 0.89568107961 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=-1.455728794\) \(a_{4}=+0.000000000\) \(a_{5}=-0.034119968\)
\(a_{6}=+0.000000000\) \(a_{7}=-0.377964473\) \(a_{8}=+0.000000000\) \(a_{9}=+1.119146321\) \(a_{10}=+0.000000000\)
\(a_{11}=+1.368293928\) \(a_{12}=+0.000000000\) \(a_{13}=+0.346127715\) \(a_{14}=+0.000000000\) \(a_{15}=+0.049669420\)
\(a_{16}=+0.000000000\) \(a_{17}=-0.374356254\) \(a_{18}=+0.000000000\) \(a_{19}=-1.442121850\) \(a_{20}=+0.000000000\)
\(a_{21}=+0.550213766\) \(a_{22}=+0.000000000\) \(a_{23}=+0.903768556\) \(a_{24}=+0.000000000\) \(a_{25}=-0.998835828\)
\(a_{26}=+0.000000000\) \(a_{27}=-0.173444731\) \(a_{28}=+0.000000000\) \(a_{29}=-0.020432861\) \(a_{30}=+0.000000000\)
\(a_{31}=+1.073408099\) \(a_{32}=+0.000000000\) \(a_{33}=-1.991864870\) \(a_{34}=+0.000000000\) \(a_{35}=+0.012896136\)
\(a_{36}=+0.000000000\) \(a_{37}=-0.320327454\) \(a_{38}=+0.000000000\) \(a_{39}=-0.503868082\) \(a_{40}=+0.000000000\)
\(a_{41}=+0.876665781\) \(a_{42}=+0.000000000\) \(a_{43}=-0.905591189\) \(a_{44}=+0.000000000\) \(a_{45}=-0.038185237\)
\(a_{46}=+0.000000000\) \(a_{47}=+0.766496629\) \(a_{48}=+0.000000000\) \(a_{49}=+0.142857143\) \(a_{50}=+0.000000000\)
\(a_{51}=+0.544961178\) \(a_{52}=+0.000000000\) \(a_{53}=+1.533830198\) \(a_{54}=+0.000000000\) \(a_{55}=-0.046686145\)
\(a_{56}=+0.000000000\) \(a_{57}=+2.099338301\) \(a_{58}=+0.000000000\) \(a_{59}=-0.780372235\) \(a_{60}=+0.000000000\)
\(a_{61}=+0.900691957\) \(a_{62}=+0.000000000\) \(a_{63}=-0.422997550\) \(a_{64}=+0.000000000\) \(a_{65}=-0.011809867\)
\(a_{66}=+0.000000000\) \(a_{67}=-0.058555295\) \(a_{68}=+0.000000000\) \(a_{69}=-1.315641910\) \(a_{70}=+0.000000000\)
\(a_{71}=-1.684788600\) \(a_{72}=+0.000000000\) \(a_{73}=-1.017869139\) \(a_{74}=+0.000000000\) \(a_{75}=+1.454034075\)
\(a_{76}=+0.000000000\) \(a_{77}=-0.517166493\) \(a_{78}=+0.000000000\) \(a_{79}=-0.033656540\) \(a_{80}=+0.000000000\)
\(a_{81}=-0.866657833\) \(a_{82}=+0.000000000\) \(a_{83}=-0.198368237\) \(a_{84}=+0.000000000\) \(a_{85}=+0.012773023\)
\(a_{86}=+0.000000000\) \(a_{87}=+0.029744704\) \(a_{88}=+0.000000000\) \(a_{89}=+0.493123236\) \(a_{90}=+0.000000000\)
\(a_{91}=-0.130823980\) \(a_{92}=+0.000000000\) \(a_{93}=-1.562591077\) \(a_{94}=+0.000000000\) \(a_{95}=+0.049205151\)
\(a_{96}=+0.000000000\) \(a_{97}=+1.557321030\) \(a_{98}=+0.000000000\) \(a_{99}=+1.531321116\) \(a_{100}=+0.000000000\)

Showing 100 of 408 available coefficients

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