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: \( 1.94743400007 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.423930808\) \(a_{3}=-0.577350269\) \(a_{4}=+1.027578946\) \(a_{5}=+0.269418524\)
\(a_{6}=-0.822106835\) \(a_{7}=+0.811570045\) \(a_{8}=+0.039270511\) \(a_{9}=+0.333333333\) \(a_{10}=+0.383633337\)
\(a_{11}=+0.350924819\) \(a_{12}=-0.593272981\) \(a_{13}=+0.786545263\) \(a_{14}=+1.155619589\) \(a_{15}=-0.155548857\)
\(a_{16}=-0.971660456\) \(a_{17}=-0.242535625\) \(a_{18}=+0.474643603\) \(a_{19}=-1.453051856\) \(a_{20}=+0.276848803\)
\(a_{21}=-0.468560184\) \(a_{22}=+0.499692660\) \(a_{23}=+1.516799094\) \(a_{24}=-0.022672840\) \(a_{25}=-0.927413659\)
\(a_{26}=+1.119986031\) \(a_{27}=-0.192450090\) \(a_{28}=+0.833952291\) \(a_{29}=+0.412515951\) \(a_{30}=-0.221490810\)
\(a_{31}=+0.045027618\) \(a_{32}=-1.422847769\) \(a_{33}=-0.202606538\) \(a_{34}=-0.345353949\) \(a_{35}=+0.218652004\)
\(a_{36}=+0.342526315\) \(a_{37}=-1.196779637\) \(a_{38}=-2.069045303\) \(a_{39}=-0.454112119\) \(a_{40}=+0.010580203\)
\(a_{41}=-0.646488471\) \(a_{42}=-0.667197281\) \(a_{43}=+1.771607314\) \(a_{44}=+0.360602955\) \(a_{45}=+0.089806175\)
\(a_{46}=+2.159816959\) \(a_{47}=+0.083336872\) \(a_{48}=+0.560988426\) \(a_{49}=-0.341354063\) \(a_{50}=-1.320572881\)
\(a_{51}=+0.140028008\) \(a_{52}=+0.808237352\) \(a_{53}=+1.516298378\) \(a_{54}=-0.274035612\) \(a_{55}=+0.094545647\)
\(a_{56}=+0.031870770\) \(a_{57}=+0.838919880\) \(a_{58}=+0.587394172\) \(a_{59}=+0.805475861\) \(a_{60}=-0.159838731\)
\(a_{61}=+0.413610634\) \(a_{62}=+0.064116213\) \(a_{63}=+0.270523348\) \(a_{64}=-1.054376317\) \(a_{65}=+0.211909864\)
\(a_{66}=-0.288497692\) \(a_{67}=-1.175899593\) \(a_{68}=-0.249224502\) \(a_{69}=-0.875724365\) \(a_{70}=+0.311345324\)
\(a_{71}=+1.627226774\) \(a_{72}=+0.013090170\) \(a_{73}=-1.810459499\) \(a_{74}=-1.704131395\) \(a_{75}=+0.535442526\)
\(a_{76}=-1.493125494\) \(a_{77}=+0.284800071\) \(a_{78}=-0.646624237\) \(a_{79}=+1.249537568\) \(a_{80}=-0.261783326\)
\(a_{81}=+0.111111111\) \(a_{82}=-0.920554850\) \(a_{83}=-1.223576118\) \(a_{84}=-0.481482580\) \(a_{85}=-0.065343590\)
\(a_{86}=+2.522646234\) \(a_{87}=-0.238166196\) \(a_{88}=+0.013780997\) \(a_{89}=-1.225225889\) \(a_{90}=+0.127877779\)
\(a_{91}=+0.638336574\) \(a_{92}=+1.558630814\) \(a_{93}=-0.025996708\) \(a_{94}=+0.118665940\) \(a_{95}=-0.391479087\)
\(a_{96}=+0.821481542\) \(a_{97}=-0.733093683\) \(a_{98}=-0.486064566\) \(a_{99}=+0.116974940\) \(a_{100}=-0.952990750\)

Showing 100 of 486 available coefficients

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