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: \( 28.7563609961 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-1.125563501\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=-0.795893584\) \(a_{7}=-0.508985762\) \(a_{8}=+0.353553391\) \(a_{9}=+0.266893194\) \(a_{10}=+0.316227766\)
\(a_{11}=-1.786276090\) \(a_{12}=-0.562781750\) \(a_{13}=+0.552266683\) \(a_{14}=-0.359907284\) \(a_{15}=-0.503367300\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.834573996\) \(a_{18}=+0.188721988\) \(a_{19}=-1.108175146\) \(a_{20}=+0.223606798\)
\(a_{21}=+0.572895796\) \(a_{22}=-1.263087936\) \(a_{23}=+1.521188423\) \(a_{24}=-0.397946792\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.390511517\) \(a_{27}=+0.825158263\) \(a_{28}=-0.254492881\) \(a_{29}=-1.740575448\) \(a_{30}=-0.355934431\)
\(a_{31}=-1.351490085\) \(a_{32}=+0.176776695\) \(a_{33}=+2.010567170\) \(a_{34}=-1.297239713\) \(a_{35}=-0.227625353\)
\(a_{36}=+0.133446597\) \(a_{37}=+0.376446823\) \(a_{38}=-0.783598161\) \(a_{39}=-0.621611221\) \(a_{40}=+0.158113883\)
\(a_{41}=-0.342442418\) \(a_{42}=+0.405098502\) \(a_{43}=+0.901175208\) \(a_{44}=-0.893138045\) \(a_{45}=+0.119358265\)
\(a_{46}=+1.075642649\) \(a_{47}=+1.113115434\) \(a_{48}=-0.281390875\) \(a_{49}=-0.740933494\) \(a_{50}=+0.141421356\)
\(a_{51}=+2.064929529\) \(a_{52}=+0.276133341\) \(a_{53}=-0.131345330\) \(a_{54}=+0.583475003\) \(a_{55}=-0.798846953\)
\(a_{56}=-0.179953642\) \(a_{57}=+1.247321497\) \(a_{58}=-1.230772702\) \(a_{59}=-1.315391130\) \(a_{60}=-0.251683650\)
\(a_{61}=+0.384719665\) \(a_{62}=-0.955647803\) \(a_{63}=-0.135844836\) \(a_{64}=+0.125000000\) \(a_{65}=+0.246981169\)
\(a_{66}=+1.421685680\) \(a_{67}=-0.880147306\) \(a_{68}=-0.917286998\) \(a_{69}=-1.712194166\) \(a_{70}=-0.160955430\)
\(a_{71}=-0.185623447\) \(a_{72}=+0.094360994\) \(a_{73}=-0.711030255\) \(a_{74}=+0.266188101\) \(a_{75}=-0.225112700\)
\(a_{76}=-0.554087573\) \(a_{77}=+0.909189097\) \(a_{78}=-0.439545510\) \(a_{79}=-1.648904369\) \(a_{80}=+0.111803399\)
\(a_{81}=-1.195661217\) \(a_{82}=-0.242143356\) \(a_{83}=-0.048557183\) \(a_{84}=+0.286447898\) \(a_{85}=-0.820446433\)
\(a_{86}=+0.637227101\) \(a_{87}=+1.959128195\) \(a_{88}=-0.631543968\) \(a_{89}=+1.695392697\) \(a_{90}=+0.084399039\)
\(a_{91}=-0.281095878\) \(a_{92}=+0.760594211\) \(a_{93}=+1.521187911\) \(a_{94}=+0.787091472\) \(a_{95}=-0.495590992\)
\(a_{96}=-0.198973396\) \(a_{97}=+0.162234300\) \(a_{98}=-0.523919098\) \(a_{99}=-0.476744932\) \(a_{100}=+0.099975586\)

Showing 100 of 240 available coefficients

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