Properties

Level $43$
Weight $0$
Character 43.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 43 \)
Weight: \( 0 \)
Character: 43.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 3.93554758484 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.000951639\) \(a_{3}=-0.458279574\) \(a_{4}=+0.001904184\) \(a_{5}=+1.584636037\)
\(a_{6}=-0.458715691\) \(a_{7}=-1.777612230\) \(a_{8}=-0.999045643\) \(a_{9}=-0.789979832\) \(a_{10}=+1.586144038\)
\(a_{11}=+0.190415725\) \(a_{12}=-0.000872649\) \(a_{13}=-1.345719825\) \(a_{14}=-1.779303875\) \(a_{15}=-0.726206328\)
\(a_{16}=-1.001900558\) \(a_{17}=+1.574773350\) \(a_{18}=-0.790731608\) \(a_{19}=-0.861910013\) \(a_{20}=+0.003017438\)
\(a_{21}=+0.814643375\) \(a_{22}=+0.190596932\) \(a_{23}=-0.315843972\) \(a_{24}=+0.457842212\) \(a_{25}=+1.511071369\)
\(a_{26}=-1.347000465\) \(a_{27}=+0.820311195\) \(a_{28}=-0.003384900\) \(a_{29}=-0.952985996\) \(a_{30}=-0.726897414\)
\(a_{31}=+0.493341535\) \(a_{32}=-0.003808362\) \(a_{33}=-0.087263637\) \(a_{34}=+1.576271966\) \(a_{35}=-2.816868399\)
\(a_{36}=-0.001504267\) \(a_{37}=+0.430376673\) \(a_{38}=-0.862730240\) \(a_{39}=+0.616715908\) \(a_{40}=-1.583123729\)
\(a_{41}=+0.139540710\) \(a_{42}=+0.815418622\) \(a_{43}=-0.152498570\) \(a_{44}=+0.000362587\) \(a_{45}=-1.251830510\)
\(a_{46}=-0.316144542\) \(a_{47}=-1.126996808\) \(a_{48}=+0.459150561\) \(a_{49}=+2.159905240\) \(a_{50}=+1.512509364\)
\(a_{51}=-0.721686460\) \(a_{52}=-0.002562498\) \(a_{53}=+0.772562187\) \(a_{54}=+0.821091835\) \(a_{55}=+0.301739620\)
\(a_{56}=+1.775915754\) \(a_{57}=+0.394995754\) \(a_{58}=-0.953892894\) \(a_{59}=-1.594901608\) \(a_{60}=-0.001382830\)
\(a_{61}=-0.380958461\) \(a_{62}=+0.493811018\) \(a_{63}=+1.404277811\) \(a_{64}=+0.998088571\) \(a_{65}=-2.132476130\)
\(a_{66}=-0.087346681\) \(a_{67}=-0.858524395\) \(a_{68}=+0.002998658\) \(a_{69}=+0.144744841\) \(a_{70}=-2.819549041\)
\(a_{71}=+1.118723867\) \(a_{72}=+0.789225910\) \(a_{73}=-0.125918586\) \(a_{74}=+0.430786236\) \(a_{75}=-0.692493143\)
\(a_{76}=-0.001641235\) \(a_{77}=-0.338485322\) \(a_{78}=+0.617302799\) \(a_{79}=-0.438588387\) \(a_{80}=-1.587647729\)
\(a_{81}=+0.414047967\) \(a_{82}=+0.139673503\) \(a_{83}=-1.220534393\) \(a_{84}=+0.001551231\) \(a_{85}=+2.495442601\)
\(a_{86}=-0.152643694\) \(a_{87}=+0.436734016\) \(a_{88}=-0.190234001\) \(a_{89}=-0.022679167\) \(a_{90}=-1.253021801\)
\(a_{91}=+2.392168019\) \(a_{92}=-0.000601425\) \(a_{93}=-0.226088348\) \(a_{94}=-1.128069302\) \(a_{95}=-1.365813667\)
\(a_{96}=+0.001745295\) \(a_{97}=-1.583901855\) \(a_{98}=+2.161960690\) \(a_{99}=-0.150424583\) \(a_{100}=+0.002877358\)

Showing 100 of 546 available coefficients

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