Properties

Level $3$
Weight $0$
Character 3.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 3 \)
Weight: \( 0 \)
Character: 3.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 4.38805356322 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.272961460\) \(a_{3}=+0.577350269\) \(a_{4}=-0.925492041\) \(a_{5}=+0.696083180\)
\(a_{6}=+0.157594378\) \(a_{7}=-0.241995809\) \(a_{8}=-0.525584913\) \(a_{9}=+0.333332055\) \(a_{10}=+0.190011730\)
\(a_{11}=+0.613619232\) \(a_{12}=-0.534333079\) \(a_{13}=-0.649728559\) \(a_{14}=-0.066055520\) \(a_{15}=+0.401883812\)
\(a_{16}=+0.782027560\) \(a_{17}=-0.285827012\) \(a_{18}=+0.090987153\) \(a_{19}=-0.381792807\) \(a_{20}=-0.644219444\)
\(a_{21}=-0.139716326\) \(a_{22}=+0.167507107\) \(a_{23}=+1.524813969\) \(a_{24}=-0.303446710\) \(a_{25}=-0.515468205\)
\(a_{26}=-0.177350856\) \(a_{27}=+0.192450090\) \(a_{28}=+0.223965164\) \(a_{29}=-1.376406133\) \(a_{30}=+0.109698792\)
\(a_{31}=+0.575459404\) \(a_{32}=+0.739048504\) \(a_{33}=+0.354300103\) \(a_{34}=-0.078019759\) \(a_{35}=-0.168449189\)
\(a_{36}=-0.308497347\) \(a_{37}=-0.555774040\) \(a_{38}=-0.104214722\) \(a_{39}=-0.375120959\) \(a_{40}=-0.365850961\)
\(a_{41}=+1.418497944\) \(a_{42}=-0.038137173\) \(a_{43}=+0.652080929\) \(a_{44}=-0.567942795\) \(a_{45}=+0.232027730\)
\(a_{46}=+0.416215451\) \(a_{47}=-1.136180387\) \(a_{48}=+0.451503818\) \(a_{49}=-0.941438038\) \(a_{50}=-0.140702944\)
\(a_{51}=-0.165022215\) \(a_{52}=+0.601318645\) \(a_{53}=+0.521278739\) \(a_{54}=+0.052531292\) \(a_{55}=+0.427162955\)
\(a_{56}=+0.127189379\) \(a_{57}=-0.220428180\) \(a_{58}=-0.375705828\) \(a_{59}=+0.577794507\) \(a_{60}=-0.371940270\)
\(a_{61}=-0.765964991\) \(a_{62}=+0.157078240\) \(a_{63}=-0.080665258\) \(a_{64}=-0.580295802\) \(a_{65}=-0.452265123\)
\(a_{66}=+0.096710274\) \(a_{67}=+1.694191670\) \(a_{68}=+0.264530625\) \(a_{69}=+0.880351753\) \(a_{70}=-0.045980138\)
\(a_{71}=-1.018776487\) \(a_{72}=-0.175195036\) \(a_{73}=-0.411307641\) \(a_{74}=-0.151704901\) \(a_{75}=-0.297605707\)
\(a_{76}=+0.353346213\) \(a_{77}=-0.148504521\) \(a_{78}=-0.102393576\) \(a_{79}=-0.740599165\) \(a_{80}=+0.544356239\)
\(a_{81}=+0.111111124\) \(a_{82}=+0.387195282\) \(a_{83}=+1.088524614\) \(a_{84}=+0.129306232\) \(a_{85}=-0.198959350\)
\(a_{86}=+0.177993022\) \(a_{87}=-0.794668566\) \(a_{88}=-0.322533499\) \(a_{89}=+0.239354854\) \(a_{90}=+0.063334571\)
\(a_{91}=+0.157233549\) \(a_{92}=-1.411202653\) \(a_{93}=+0.332242620\) \(a_{94}=-0.310133567\) \(a_{95}=-0.265759906\)
\(a_{96}=+0.426689852\) \(a_{97}=+1.046722859\) \(a_{98}=-0.256976304\) \(a_{99}=+0.204555261\) \(a_{100}=+0.477061719\)

Showing 100 of 5000 available coefficients

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