Properties

Level $10$
Weight $0$
Character 10.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 10 = 2 \cdot 5 \)
Weight: \( 0 \)
Character: 10.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 31.2255274723 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+1.529405527\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=-1.081453019\) \(a_{7}=-1.409426962\) \(a_{8}=-0.353553391\) \(a_{9}=+1.339081265\) \(a_{10}=+0.316227766\)
\(a_{11}=-1.531594264\) \(a_{12}=+0.764702763\) \(a_{13}=-1.423619259\) \(a_{14}=+0.996615362\) \(a_{15}=-0.683970945\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.263871577\) \(a_{18}=-0.946873443\) \(a_{19}=-0.574630845\) \(a_{20}=-0.223606798\)
\(a_{21}=-2.155585385\) \(a_{22}=+1.083000690\) \(a_{23}=+0.811192759\) \(a_{24}=-0.540726510\) \(a_{25}=+0.199951172\)
\(a_{26}=+1.006650832\) \(a_{27}=+0.518592761\) \(a_{28}=-0.704713481\) \(a_{29}=+1.453621419\) \(a_{30}=+0.483640493\)
\(a_{31}=-1.297330961\) \(a_{32}=-0.176776695\) \(a_{33}=-2.342428732\) \(a_{34}=-0.893692162\) \(a_{35}=+0.630314899\)
\(a_{36}=+0.669540633\) \(a_{37}=-0.468166475\) \(a_{38}=+0.406325367\) \(a_{39}=-2.177291162\) \(a_{40}=+0.158113883\)
\(a_{41}=-1.475689150\) \(a_{42}=+1.524229043\) \(a_{43}=-1.726741059\) \(a_{44}=-0.765797132\) \(a_{45}=-0.598855347\)
\(a_{46}=-0.573599901\) \(a_{47}=-0.811725550\) \(a_{48}=+0.382351382\) \(a_{49}=+0.986484360\) \(a_{50}=-0.141421356\)
\(a_{51}=+1.932972175\) \(a_{52}=-0.711809629\) \(a_{53}=-0.187710383\) \(a_{54}=-0.366700458\) \(a_{55}=+0.684949778\)
\(a_{56}=+0.498307681\) \(a_{57}=-0.878843590\) \(a_{58}=-1.027865562\) \(a_{59}=-0.439605001\) \(a_{60}=-0.341985472\)
\(a_{61}=+0.022400617\) \(a_{62}=+0.917351520\) \(a_{63}=-1.887337239\) \(a_{64}=+0.125000000\) \(a_{65}=+0.636661887\)
\(a_{66}=+1.656347241\) \(a_{67}=+0.132479792\) \(a_{68}=+0.631935788\) \(a_{69}=+1.240642689\) \(a_{70}=-0.445699939\)
\(a_{71}=+1.395274424\) \(a_{72}=-0.473436722\) \(a_{73}=-1.166806694\) \(a_{74}=+0.331043689\) \(a_{75}=+0.305881105\)
\(a_{76}=-0.287315423\) \(a_{77}=+2.158670250\) \(a_{78}=+1.539577345\) \(a_{79}=-0.430396712\) \(a_{80}=-0.111803399\)
\(a_{81}=-0.545942630\) \(a_{82}=+1.043469805\) \(a_{83}=+1.218009833\) \(a_{84}=-1.077792692\) \(a_{85}=-0.565220552\)
\(a_{86}=+1.220990312\) \(a_{87}=+2.223176631\) \(a_{88}=+0.541500345\) \(a_{89}=+0.021998733\) \(a_{90}=+0.423454677\)
\(a_{91}=+2.006487366\) \(a_{92}=+0.405596379\) \(a_{93}=-1.984145141\) \(a_{94}=+0.573976641\) \(a_{95}=+0.256982726\)
\(a_{96}=-0.270363255\) \(a_{97}=+0.303573563\) \(a_{98}=-0.697549781\) \(a_{99}=-2.050929184\) \(a_{100}=+0.099975586\)

Showing 100 of 250 available coefficients

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