Properties

Level $3$
Weight $0$
Character 3.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 3 \)
Weight: \( 0 \)
Character: 3.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 27.6410466219 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.497279429\) \(a_{3}=-0.577350269\) \(a_{4}=+1.241845689\) \(a_{5}=+0.350597034\)
\(a_{6}=+0.864454681\) \(a_{7}=-1.713577338\) \(a_{8}=-0.362110575\) \(a_{9}=+0.333333333\) \(a_{10}=-0.524941727\)
\(a_{11}=+1.094119549\) \(a_{12}=-0.716979943\) \(a_{13}=+1.011827605\) \(a_{14}=+2.565704098\) \(a_{15}=-0.202417292\)
\(a_{16}=-0.699664974\) \(a_{17}=-0.540648835\) \(a_{18}=-0.499093143\) \(a_{19}=+0.432998592\) \(a_{20}=+0.435387415\)
\(a_{21}=+0.989334337\) \(a_{22}=-1.638202694\) \(a_{23}=+0.457070960\) \(a_{24}=+0.209064638\) \(a_{25}=-0.877081720\)
\(a_{26}=-1.514988659\) \(a_{27}=-0.192450090\) \(a_{28}=-2.127998630\) \(a_{29}=-1.013080427\) \(a_{30}=+0.303075247\)
\(a_{31}=-1.563196086\) \(a_{32}=+1.409704548\) \(a_{33}=-0.631690216\) \(a_{34}=+0.809502379\) \(a_{35}=-0.600775132\)
\(a_{36}=+0.413948563\) \(a_{37}=+0.473524349\) \(a_{38}=-0.648319885\) \(a_{39}=-0.584178940\) \(a_{40}=-0.126954894\)
\(a_{41}=-1.424649868\) \(a_{42}=-1.481309952\) \(a_{43}=+1.035294434\) \(a_{44}=+1.358727645\) \(a_{45}=+0.116865678\)
\(a_{46}=-0.684362946\) \(a_{47}=-1.455226556\) \(a_{48}=+0.403951761\) \(a_{49}=+1.936347292\) \(a_{50}=+1.313236417\)
\(a_{51}=+0.312143750\) \(a_{52}=+1.256533749\) \(a_{53}=-0.134824966\) \(a_{54}=+0.288151560\) \(a_{55}=+0.383595069\)
\(a_{56}=+0.620504475\) \(a_{57}=-0.249991854\) \(a_{58}=+1.516864483\) \(a_{59}=+1.112884784\) \(a_{60}=-0.251371041\)
\(a_{61}=-0.690166840\) \(a_{62}=+2.340541344\) \(a_{63}=-0.571192446\) \(a_{64}=-1.411056647\) \(a_{65}=+0.354743757\)
\(a_{66}=+0.945816766\) \(a_{67}=+0.756445590\) \(a_{68}=-0.671402425\) \(a_{69}=-0.263890042\) \(a_{70}=+0.899528247\)
\(a_{71}=-0.546174931\) \(a_{72}=-0.120703525\) \(a_{73}=+1.138277026\) \(a_{74}=-0.708998266\) \(a_{75}=+0.506383367\)
\(a_{76}=+0.537717435\) \(a_{77}=-1.874858464\) \(a_{78}=+0.874679110\) \(a_{79}=-0.842496420\) \(a_{80}=-0.245300465\)
\(a_{81}=+0.111111111\) \(a_{82}=+2.133098941\) \(a_{83}=-0.904332049\) \(a_{84}=+1.228600582\) \(a_{85}=-0.189549878\)
\(a_{86}=-1.550125060\) \(a_{87}=+0.584902257\) \(a_{88}=-0.396192259\) \(a_{89}=-0.096380983\) \(a_{90}=-0.174980576\)
\(a_{91}=-1.733844854\) \(a_{92}=+0.567611601\) \(a_{93}=+0.902511681\) \(a_{94}=+2.178880787\) \(a_{95}=+0.151808022\)
\(a_{96}=-0.813893300\) \(a_{97}=+1.649877253\) \(a_{98}=-2.899252968\) \(a_{99}=+0.364706516\) \(a_{100}=-1.089200152\)

Showing 100 of 1228 available coefficients

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