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: \( 11.3659037782 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.669557524\) \(a_{3}=-0.577350269\) \(a_{4}=+1.787422325\) \(a_{5}=+1.102846203\)
\(a_{6}=+0.963919486\) \(a_{7}=-0.810915498\) \(a_{8}=-1.314646866\) \(a_{9}=+0.333333334\) \(a_{10}=-1.841265177\)
\(a_{11}=+1.027594863\) \(a_{12}=-1.031968778\) \(a_{13}=-0.783350960\) \(a_{14}=+1.353869623\) \(a_{15}=-0.636726511\)
\(a_{16}=+0.407447784\) \(a_{17}=-0.581874630\) \(a_{18}=-0.556519175\) \(a_{19}=-0.282312536\) \(a_{20}=+1.971251925\)
\(a_{21}=+0.468182281\) \(a_{22}=-1.715628729\) \(a_{23}=-1.046483928\) \(a_{24}=+0.759011722\) \(a_{25}=+0.216269748\)
\(a_{26}=+1.307849639\) \(a_{27}=-0.192450090\) \(a_{28}=-1.449448465\) \(a_{29}=+0.345206895\) \(a_{30}=+1.063054945\)
\(a_{31}=-1.396910407\) \(a_{32}=+0.634375232\) \(a_{33}=-0.593282169\) \(a_{34}=+0.971473167\) \(a_{35}=-0.894315079\)
\(a_{36}=+0.595807442\) \(a_{37}=+0.145072395\) \(a_{38}=+0.471337019\) \(a_{39}=+0.452267939\) \(a_{40}=-1.449853305\)
\(a_{41}=-0.193489748\) \(a_{42}=-0.781657250\) \(a_{43}=-0.447173065\) \(a_{44}=+1.836745992\) \(a_{45}=+0.367615401\)
\(a_{46}=+1.747165115\) \(a_{47}=-1.744650788\) \(a_{48}=-0.235244971\) \(a_{49}=-0.342416054\) \(a_{50}=-0.361074787\)
\(a_{51}=+0.335945474\) \(a_{52}=-1.400179152\) \(a_{53}=+0.483898974\) \(a_{54}=+0.321306496\) \(a_{55}=+1.133279078\)
\(a_{56}=+1.066067526\) \(a_{57}=+0.162993229\) \(a_{58}=-0.576342762\) \(a_{59}=-1.970235396\) \(a_{60}=-1.138102890\)
\(a_{61}=+1.211433744\) \(a_{62}=+2.332222294\) \(a_{63}=-0.270305166\) \(a_{64}=-1.466582183\) \(a_{65}=-0.863915731\)
\(a_{66}=+0.990518708\) \(a_{67}=-0.318653983\) \(a_{68}=-1.040055704\) \(a_{69}=+0.604187778\) \(a_{70}=+1.493110468\)
\(a_{71}=+0.897569307\) \(a_{72}=-0.438215622\) \(a_{73}=-0.267922729\) \(a_{74}=-0.242206709\) \(a_{75}=-0.124863397\)
\(a_{76}=-0.504611730\) \(a_{77}=-0.833292598\) \(a_{78}=-0.755087342\) \(a_{79}=+0.285255160\) \(a_{80}=+0.449361571\)
\(a_{81}=+0.111111112\) \(a_{82}=+0.323042263\) \(a_{83}=+1.230889079\) \(a_{84}=+0.836839464\) \(a_{85}=-0.641718222\)
\(a_{86}=+0.746581156\) \(a_{87}=-0.199305303\) \(a_{88}=-1.350924366\) \(a_{89}=-0.764682647\) \(a_{90}=-0.613755045\)
\(a_{91}=+0.635231494\) \(a_{92}=-1.870508767\) \(a_{93}=+0.806506607\) \(a_{94}=+2.912794903\) \(a_{95}=-0.311347287\)
\(a_{96}=-0.366256793\) \(a_{97}=-1.461418483\) \(a_{98}=+0.571683400\) \(a_{99}=+0.342531811\) \(a_{100}=+0.386565329\)

Showing 100 of 5000 available coefficients

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