Properties

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

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Maass form invariants

Level: \( 51 = 3 \cdot 17 \)
Weight: \( 0 \)
Character: 51.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 3.11757306367 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.021301605\) \(a_{3}=-0.577350269\) \(a_{4}=+0.043056968\) \(a_{5}=-1.765888618\)
\(a_{6}=+0.589648756\) \(a_{7}=-1.119498562\) \(a_{8}=+0.977327454\) \(a_{9}=+0.333333333\) \(a_{10}=+1.803504879\)
\(a_{11}=+0.800644349\) \(a_{12}=-0.024858952\) \(a_{13}=-1.524571207\) \(a_{14}=+1.143345677\) \(a_{15}=+1.019536269\)
\(a_{16}=-1.041203065\) \(a_{17}=+0.242535625\) \(a_{18}=-0.340433868\) \(a_{19}=-0.960314570\) \(a_{20}=-0.076033809\)
\(a_{21}=+0.646342796\) \(a_{22}=-0.817699358\) \(a_{23}=-1.278480207\) \(a_{24}=-0.564260269\) \(a_{25}=+2.118362611\)
\(a_{26}=+1.557047020\) \(a_{27}=-0.192450090\) \(a_{28}=-0.048202214\) \(a_{29}=+0.924910181\) \(a_{30}=-1.041254027\)
\(a_{31}=-0.730315538\) \(a_{32}=+0.086054907\) \(a_{33}=-0.462252230\) \(a_{34}=-0.247702023\) \(a_{35}=+1.976909768\)
\(a_{36}=+0.014352323\) \(a_{37}=-0.168628130\) \(a_{38}=+0.980770811\) \(a_{39}=+0.880211597\) \(a_{40}=-1.725851428\)
\(a_{41}=+0.516422297\) \(a_{42}=-0.660110935\) \(a_{43}=+1.163473176\) \(a_{44}=+0.034473318\) \(a_{45}=-0.588629539\)
\(a_{46}=+1.305713887\) \(a_{47}=-0.776975791\) \(a_{48}=+0.601138870\) \(a_{49}=+0.253277030\) \(a_{50}=-2.163487133\)
\(a_{51}=-0.140028008\) \(a_{52}=-0.065643413\) \(a_{53}=+0.128828088\) \(a_{54}=+0.196549585\) \(a_{55}=-1.413848742\)
\(a_{56}=-1.094116679\) \(a_{57}=+0.554437875\) \(a_{58}=-0.944612252\) \(a_{59}=+0.403577347\) \(a_{60}=+0.043898140\)
\(a_{61}=-1.075317503\) \(a_{62}=+0.745872431\) \(a_{63}=-0.373166187\) \(a_{64}=+0.953315051\) \(a_{65}=+2.692222942\)
\(a_{66}=+0.472098945\) \(a_{67}=+1.401209922\) \(a_{68}=+0.010442849\) \(a_{69}=+0.738130892\) \(a_{70}=-2.019021118\)
\(a_{71}=-0.586364562\) \(a_{72}=+0.325775818\) \(a_{73}=-1.246331661\) \(a_{74}=+0.172220179\) \(a_{75}=-1.223037223\)
\(a_{76}=-0.041348233\) \(a_{77}=-0.896320197\) \(a_{78}=-0.898961516\) \(a_{79}=+0.838428348\) \(a_{80}=+1.838648642\)
\(a_{81}=+0.111111111\) \(a_{82}=-0.527422921\) \(a_{83}=-0.450764455\) \(a_{84}=+0.027829561\) \(a_{85}=-0.428290900\)
\(a_{86}=-1.188257021\) \(a_{87}=-0.533997142\) \(a_{88}=+0.782491703\) \(a_{89}=+1.188905225\) \(a_{90}=+0.601168293\)
\(a_{91}=+1.706755273\) \(a_{92}=-0.055047481\) \(a_{93}=+0.421647872\) \(a_{94}=+0.793526622\) \(a_{95}=+1.695808568\)
\(a_{96}=-0.049683824\) \(a_{97}=-0.982618007\) \(a_{98}=-0.258672237\) \(a_{99}=+0.266881450\) \(a_{100}=+0.091210271\)

Showing 100 of 460 available coefficients

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