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: \( 3.7323620972 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.136676488\) \(a_{3}=+0.577350269\) \(a_{4}=-0.981319538\) \(a_{5}=-1.352026280\)
\(a_{6}=-0.078910207\) \(a_{7}=+1.534624756\) \(a_{8}=+0.270799796\) \(a_{9}=+0.333333333\) \(a_{10}=+0.184790204\)
\(a_{11}=+1.195076104\) \(a_{12}=-0.566565099\) \(a_{13}=-0.855309864\) \(a_{14}=-0.209747122\) \(a_{15}=-0.780592736\)
\(a_{16}=+0.944307572\) \(a_{17}=+0.242535625\) \(a_{18}=-0.045558829\) \(a_{19}=+1.111521327\) \(a_{20}=+1.326769804\)
\(a_{21}=+0.886016016\) \(a_{22}=-0.163338805\) \(a_{23}=-0.808439121\) \(a_{24}=+0.156346335\) \(a_{25}=+0.827975061\)
\(a_{26}=+0.116900749\) \(a_{27}=+0.192450090\) \(a_{28}=-1.505957256\) \(a_{29}=+0.698803523\) \(a_{30}=+0.106688674\)
\(a_{31}=+1.624740111\) \(a_{32}=-0.399864439\) \(a_{33}=+0.689977511\) \(a_{34}=-0.033148917\) \(a_{35}=-2.074852999\)
\(a_{36}=-0.327106513\) \(a_{37}=+0.138659266\) \(a_{38}=-0.151918831\) \(a_{39}=-0.493813381\) \(a_{40}=-0.366128441\)
\(a_{41}=+1.509211439\) \(a_{42}=-0.121097557\) \(a_{43}=+1.122094870\) \(a_{44}=-1.172751530\) \(a_{45}=-0.450675427\)
\(a_{46}=+0.110494620\) \(a_{47}=-1.544490416\) \(a_{48}=+0.545196231\) \(a_{49}=+1.355073141\) \(a_{50}=-0.113164724\)
\(a_{51}=+0.140028008\) \(a_{52}=+0.839332281\) \(a_{53}=-0.977806190\) \(a_{54}=-0.026303402\) \(a_{55}=-1.615774299\)
\(a_{56}=+0.415576071\) \(a_{57}=+0.641737137\) \(a_{58}=-0.095510011\) \(a_{59}=-0.434438833\) \(a_{60}=+0.766010903\)
\(a_{61}=+0.835527353\) \(a_{62}=-0.222063772\) \(a_{63}=+0.511541585\) \(a_{64}=-0.889655505\) \(a_{65}=+1.156401414\)
\(a_{66}=-0.094303703\) \(a_{67}=+0.792892508\) \(a_{68}=-0.238004947\) \(a_{69}=-0.466752544\) \(a_{70}=+0.283583621\)
\(a_{71}=+0.569740757\) \(a_{72}=+0.090266599\) \(a_{73}=+0.470383397\) \(a_{74}=-0.018951462\) \(a_{75}=+0.478031624\)
\(a_{76}=-1.090757595\) \(a_{77}=+1.833993375\) \(a_{78}=+0.067492679\) \(a_{79}=-0.646405900\) \(a_{80}=-1.276728654\)
\(a_{81}=+0.111111111\) \(a_{82}=-0.206273719\) \(a_{83}=-0.535455074\) \(a_{84}=-0.869464827\) \(a_{85}=-0.327914539\)
\(a_{86}=-0.153363986\) \(a_{87}=+0.403454402\) \(a_{88}=+0.323626365\) \(a_{89}=-1.022142837\) \(a_{90}=+0.061596735\)
\(a_{91}=-1.312579692\) \(a_{92}=+0.793337104\) \(a_{93}=+0.938044140\) \(a_{94}=+0.211095526\) \(a_{95}=-1.502806045\)
\(a_{96}=-0.230861841\) \(a_{97}=+1.235130097\) \(a_{98}=-0.185206638\) \(a_{99}=+0.398358701\) \(a_{100}=-0.812508104\)

Showing 100 of 466 available coefficients

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