Properties

Level $53$
Weight $0$
Character 53.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 53 \)
Weight: \( 0 \)
Character: 53.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 1.0158404282 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.547887663\) \(a_{3}=+0.012236671\) \(a_{4}=-0.699819109\) \(a_{5}=-0.251391187\)
\(a_{6}=-0.006704321\) \(a_{7}=+0.352259076\) \(a_{8}=+0.931309918\) \(a_{9}=-0.999850264\) \(a_{10}=+0.137734130\)
\(a_{11}=+0.989512943\) \(a_{12}=-0.008563456\) \(a_{13}=+0.399573229\) \(a_{14}=-0.192998402\) \(a_{15}=-0.003076191\)
\(a_{16}=+0.189565895\) \(a_{17}=+1.622164057\) \(a_{18}=+0.547805624\) \(a_{19}=-1.143666249\) \(a_{20}=+0.175928356\)
\(a_{21}=+0.004310479\) \(a_{22}=-0.542141933\) \(a_{23}=-1.071810416\) \(a_{24}=+0.011396133\) \(a_{25}=-0.936802471\)
\(a_{26}=-0.218921242\) \(a_{27}=-0.024471511\) \(a_{28}=-0.246517633\) \(a_{29}=+1.234244497\) \(a_{30}=+0.001685407\)
\(a_{31}=-0.895460244\) \(a_{32}=-1.035170734\) \(a_{33}=+0.012108345\) \(a_{34}=-0.888763674\) \(a_{35}=-0.088554827\)
\(a_{36}=+0.699714321\) \(a_{37}=+0.517801708\) \(a_{38}=+0.626600628\) \(a_{39}=+0.004889446\) \(a_{40}=-0.234123105\)
\(a_{41}=+0.977303717\) \(a_{42}=-0.002361658\) \(a_{43}=+1.125154027\) \(a_{44}=-0.692480066\) \(a_{45}=+0.251353544\)
\(a_{46}=+0.587231704\) \(a_{47}=+0.394683055\) \(a_{48}=+0.002319656\) \(a_{49}=-0.875913543\) \(a_{50}=+0.513262516\)
\(a_{51}=+0.019849889\) \(a_{52}=-0.279628981\) \(a_{53}=-0.137360564\) \(a_{54}=+0.013407639\) \(a_{55}=-0.248754833\)
\(a_{56}=+0.328062372\) \(a_{57}=-0.013994668\) \(a_{58}=-0.676227332\) \(a_{59}=+0.301434426\) \(a_{60}=+0.002152777\)
\(a_{61}=+1.577187757\) \(a_{62}=+0.490611620\) \(a_{63}=-0.352206330\) \(a_{64}=+0.377591379\) \(a_{65}=-0.100449188\)
\(a_{66}=-0.006634013\) \(a_{67}=-0.699344559\) \(a_{68}=-1.135221406\) \(a_{69}=-0.013115392\) \(a_{70}=+0.048518097\)
\(a_{71}=-0.838699432\) \(a_{72}=-0.931170468\) \(a_{73}=+0.801385866\) \(a_{74}=-0.283697168\) \(a_{75}=-0.011463344\)
\(a_{76}=+0.800359496\) \(a_{77}=+0.348564915\) \(a_{78}=-0.002678867\) \(a_{79}=-0.073110008\) \(a_{80}=-0.047655195\)
\(a_{81}=+0.999550814\) \(a_{82}=-0.535452649\) \(a_{83}=-1.632662250\) \(a_{84}=-0.003016555\) \(a_{85}=-0.407797747\)
\(a_{86}=-0.616458010\) \(a_{87}=+0.015103044\) \(a_{88}=+0.921543218\) \(a_{89}=-1.048401409\) \(a_{90}=-0.137713506\)
\(a_{91}=+0.140753297\) \(a_{92}=+0.750073411\) \(a_{93}=-0.010957453\) \(a_{94}=-0.216241977\) \(a_{95}=+0.287507615\)
\(a_{96}=-0.012667044\) \(a_{97}=-1.111989766\) \(a_{98}=+0.479902224\) \(a_{99}=-0.989364777\) \(a_{100}=+0.655592271\)

Showing 100 of 546 available coefficients

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