Properties

Level $52$
Weight $0$
Character 52.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 52 = 2^{2} \cdot 13 \)
Weight: \( 0 \)
Character: 52.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 2.06042352995 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=+0.208373426\) \(a_{4}=+0.000000000\) \(a_{5}=+1.572956845\)
\(a_{6}=+0.000000000\) \(a_{7}=+1.379248515\) \(a_{8}=+0.000000000\) \(a_{9}=-0.956580516\) \(a_{10}=+0.000000000\)
\(a_{11}=+0.514067052\) \(a_{12}=+0.000000000\) \(a_{13}=-0.277350098\) \(a_{14}=+0.000000000\) \(a_{15}=+0.327762406\)
\(a_{16}=+0.000000000\) \(a_{17}=-1.635419979\) \(a_{18}=+0.000000000\) \(a_{19}=+0.356828939\) \(a_{20}=+0.000000000\)
\(a_{21}=+0.287398738\) \(a_{22}=+0.000000000\) \(a_{23}=-0.966110897\) \(a_{24}=+0.000000000\) \(a_{25}=+1.474193236\)
\(a_{26}=+0.000000000\) \(a_{27}=-0.407699384\) \(a_{28}=+0.000000000\) \(a_{29}=+0.713878583\) \(a_{30}=+0.000000000\)
\(a_{31}=-0.018073415\) \(a_{32}=+0.000000000\) \(a_{33}=+0.107117913\) \(a_{34}=+0.000000000\) \(a_{35}=+2.169498393\)
\(a_{36}=+0.000000000\) \(a_{37}=+0.458266571\) \(a_{38}=+0.000000000\) \(a_{39}=-0.057792390\) \(a_{40}=+0.000000000\)
\(a_{41}=-1.770384098\) \(a_{42}=+0.000000000\) \(a_{43}=-1.076647304\) \(a_{44}=+0.000000000\) \(a_{45}=-1.504659870\)
\(a_{46}=+0.000000000\) \(a_{47}=+1.312533980\) \(a_{48}=+0.000000000\) \(a_{49}=+0.902326466\) \(a_{50}=+0.000000000\)
\(a_{51}=-0.340778063\) \(a_{52}=+0.000000000\) \(a_{53}=-0.827227303\) \(a_{54}=+0.000000000\) \(a_{55}=+0.808605288\)
\(a_{56}=+0.000000000\) \(a_{57}=+0.074353668\) \(a_{58}=+0.000000000\) \(a_{59}=-0.543355341\) \(a_{60}=+0.000000000\)
\(a_{61}=-0.676600605\) \(a_{62}=+0.000000000\) \(a_{63}=-1.319362256\) \(a_{64}=+0.000000000\) \(a_{65}=-0.436259735\)
\(a_{66}=+0.000000000\) \(a_{67}=+0.603641653\) \(a_{68}=+0.000000000\) \(a_{69}=-0.201311837\) \(a_{70}=+0.000000000\)
\(a_{71}=-0.405728501\) \(a_{72}=+0.000000000\) \(a_{73}=+1.525231895\) \(a_{74}=+0.000000000\) \(a_{75}=+0.307182695\)
\(a_{76}=+0.000000000\) \(a_{77}=+0.709026218\) \(a_{78}=+0.000000000\) \(a_{79}=+1.650932288\) \(a_{80}=+0.000000000\)
\(a_{81}=+0.871626798\) \(a_{82}=+0.000000000\) \(a_{83}=+0.967572172\) \(a_{84}=+0.000000000\) \(a_{85}=-2.572445050\)
\(a_{86}=+0.000000000\) \(a_{87}=+0.148753326\) \(a_{88}=+0.000000000\) \(a_{89}=+0.819251270\) \(a_{90}=+0.000000000\)
\(a_{91}=-0.382534711\) \(a_{92}=+0.000000000\) \(a_{93}=-0.003766019\) \(a_{94}=+0.000000000\) \(a_{95}=+0.561276522\)
\(a_{96}=+0.000000000\) \(a_{97}=-0.722303343\) \(a_{98}=+0.000000000\) \(a_{99}=-0.491746525\) \(a_{100}=+0.000000000\)

Showing 100 of 388 available coefficients

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