Properties

Level $51$
Weight $0$
Character 51.1
Symmetry even
Fricke sign $-1$

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Maass form invariants

Level: \( 51 = 3 \cdot 17 \)
Weight: \( 0 \)
Character: 51.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 1.85512497428 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.513896645\) \(a_{3}=-0.577350269\) \(a_{4}=+1.291883050\) \(a_{5}=-0.804009625\)
\(a_{6}=+0.874048635\) \(a_{7}=+0.891673426\) \(a_{8}=-0.441880770\) \(a_{9}=+0.333333333\) \(a_{10}=+1.217187474\)
\(a_{11}=-1.509678004\) \(a_{12}=-0.745869027\) \(a_{13}=-0.835989901\) \(a_{14}=-1.349901408\) \(a_{15}=+0.464195174\)
\(a_{16}=-0.622921235\) \(a_{17}=+0.242535625\) \(a_{18}=-0.504632215\) \(a_{19}=+0.441756328\) \(a_{20}=-1.038686407\)
\(a_{21}=-0.514807893\) \(a_{22}=+2.285496464\) \(a_{23}=+0.981976315\) \(a_{24}=+0.255119982\) \(a_{25}=-0.353568522\)
\(a_{26}=+1.265602306\) \(a_{27}=-0.192450090\) \(a_{28}=+1.151937785\) \(a_{29}=-0.724440507\) \(a_{30}=-0.702743516\)
\(a_{31}=-1.846996920\) \(a_{32}=+1.384919137\) \(a_{33}=+0.871613002\) \(a_{34}=-0.367173869\) \(a_{35}=-0.716914017\)
\(a_{36}=+0.430627683\) \(a_{37}=+0.587779161\) \(a_{38}=-0.668773423\) \(a_{39}=+0.482658994\) \(a_{40}=+0.355276393\)
\(a_{41}=+1.587837137\) \(a_{42}=+0.779365941\) \(a_{43}=-0.636963651\) \(a_{44}=-1.950327424\) \(a_{45}=-0.268003208\)
\(a_{46}=-1.486610648\) \(a_{47}=-1.710817562\) \(a_{48}=+0.359643742\) \(a_{49}=-0.204918501\) \(a_{50}=+0.535266200\)
\(a_{51}=-0.140028008\) \(a_{52}=-1.080001183\) \(a_{53}=-0.305167694\) \(a_{54}=+0.291349545\) \(a_{55}=+1.213795646\)
\(a_{56}=-0.394013340\) \(a_{57}=-0.255048135\) \(a_{58}=+1.096728052\) \(a_{59}=-1.255370481\) \(a_{60}=+0.599685877\)
\(a_{61}=+1.166443394\) \(a_{62}=+2.796162439\) \(a_{63}=+0.297224475\) \(a_{64}=-1.473703200\) \(a_{65}=+0.672143927\)
\(a_{66}=-1.319531999\) \(a_{67}=-0.716273338\) \(a_{68}=+0.313327663\) \(a_{69}=-0.566944290\) \(a_{70}=+1.085333725\)
\(a_{71}=+0.605016811\) \(a_{72}=-0.147293590\) \(a_{73}=+1.026090458\) \(a_{74}=-0.889836900\) \(a_{75}=+0.204132882\)
\(a_{76}=+0.570697513\) \(a_{77}=-1.346139758\) \(a_{78}=-0.730695832\) \(a_{79}=-0.689677248\) \(a_{80}=+0.500834668\)
\(a_{81}=+0.111111111\) \(a_{82}=-2.403821314\) \(a_{83}=+0.537026776\) \(a_{84}=-0.665071591\) \(a_{85}=-0.195000977\)
\(a_{86}=+0.964297134\) \(a_{87}=+0.418255922\) \(a_{88}=+0.667097679\) \(a_{89}=+0.261634799\) \(a_{90}=+0.405729158\)
\(a_{91}=-0.745429979\) \(a_{92}=+1.268598557\) \(a_{93}=+1.066364169\) \(a_{94}=+2.590000966\) \(a_{95}=-0.355176340\)
\(a_{96}=-0.799583437\) \(a_{97}=+0.712146797\) \(a_{98}=+0.310225432\) \(a_{99}=-0.503226001\) \(a_{100}=-0.456769181\)

Showing 100 of 520 available coefficients

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