Properties

Level $65$
Weight $0$
Character 65.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 65 = 5 \cdot 13 \)
Weight: \( 0 \)
Character: 65.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 0.77947156173 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.396874315\) \(a_{3}=-1.674379275\) \(a_{4}=-0.842490778\) \(a_{5}=+0.447213596\)
\(a_{6}=-0.664518127\) \(a_{7}=+0.612592949\) \(a_{8}=-0.731237265\) \(a_{9}=+1.803545956\) \(a_{10}=+0.177487589\)
\(a_{11}=-0.323690876\) \(a_{12}=+1.410649099\) \(a_{13}=+0.277350098\) \(a_{14}=+0.243122407\) \(a_{15}=-0.748805176\)
\(a_{16}=+0.552281490\) \(a_{17}=+0.029947057\) \(a_{18}=+0.715781065\) \(a_{19}=-1.499153626\) \(a_{20}=-0.376773330\)
\(a_{21}=-1.025712938\) \(a_{22}=-0.128464594\) \(a_{23}=+0.311052610\) \(a_{24}=+1.224368521\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.110073130\) \(a_{27}=-1.345440694\) \(a_{28}=-0.516103911\) \(a_{29}=+1.520260597\) \(a_{30}=-0.297181541\)
\(a_{31}=-0.090782917\) \(a_{32}=+0.950423603\) \(a_{33}=+0.541981294\) \(a_{34}=+0.011885218\) \(a_{35}=+0.273959895\)
\(a_{36}=-1.519470836\) \(a_{37}=-0.959073592\) \(a_{38}=-0.594975568\) \(a_{39}=-0.464389256\) \(a_{40}=-0.327019246\)
\(a_{41}=+0.568953919\) \(a_{42}=-0.407079119\) \(a_{43}=-0.378153495\) \(a_{44}=+0.272706578\) \(a_{45}=+0.806570271\)
\(a_{46}=+0.123448791\) \(a_{47}=+0.178527785\) \(a_{48}=-0.924728681\) \(a_{49}=-0.624729879\) \(a_{50}=+0.079374863\)
\(a_{51}=-0.050142731\) \(a_{52}=-0.233664900\) \(a_{53}=+0.603654954\) \(a_{54}=-0.533970853\) \(a_{55}=-0.144758960\)
\(a_{56}=-0.447950793\) \(a_{57}=+2.510151761\) \(a_{58}=+0.603352382\) \(a_{59}=-0.749182688\) \(a_{60}=+0.630861455\)
\(a_{61}=+1.010517886\) \(a_{62}=-0.036029408\) \(a_{63}=+1.104839536\) \(a_{64}=-0.175082774\) \(a_{65}=+0.124034735\)
\(a_{66}=+0.215098455\) \(a_{67}=+0.718951043\) \(a_{68}=-0.025230119\) \(a_{69}=-0.520820044\) \(a_{70}=+0.108727646\)
\(a_{71}=+1.664761666\) \(a_{72}=-1.318820011\) \(a_{73}=-1.884859210\) \(a_{74}=-0.380631674\) \(a_{75}=-0.334875855\)
\(a_{76}=+1.263023106\) \(a_{77}=-0.198290748\) \(a_{78}=-0.184304168\) \(a_{79}=+1.009422354\) \(a_{80}=+0.246987791\)
\(a_{81}=+0.449232058\) \(a_{82}=+0.225803197\) \(a_{83}=-0.615623277\) \(a_{84}=+0.864153692\) \(a_{85}=+0.013392731\)
\(a_{86}=-0.150079409\) \(a_{87}=-2.545492836\) \(a_{88}=+0.236694831\) \(a_{89}=-0.972677335\) \(a_{90}=+0.320107024\)
\(a_{91}=+0.169902715\) \(a_{92}=-0.262058956\) \(a_{93}=+0.152005035\) \(a_{94}=+0.070853092\) \(a_{95}=-0.670441883\)
\(a_{96}=-1.591369582\) \(a_{97}=-1.809382932\) \(a_{98}=-0.247939242\) \(a_{99}=-0.583791370\) \(a_{100}=-0.168498156\)

Showing 100 of 462 available coefficients

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