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: \( 23.4601771307 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.213777906\) \(a_{3}=-0.577350269\) \(a_{4}=+0.473256805\) \(a_{5}=-0.291181476\)
\(a_{6}=-0.700775001\) \(a_{7}=+1.315337954\) \(a_{8}=-0.639349253\) \(a_{9}=+0.333333333\) \(a_{10}=-0.353429642\)
\(a_{11}=-0.449310198\) \(a_{12}=-0.273234944\) \(a_{13}=+0.884012453\) \(a_{14}=+1.596528147\) \(a_{15}=+0.168113703\)
\(a_{16}=-1.249284802\) \(a_{17}=-0.247072287\) \(a_{18}=+0.404592635\) \(a_{19}=-1.504530422\) \(a_{20}=-0.137803615\)
\(a_{21}=-0.759410722\) \(a_{22}=-0.545362791\) \(a_{23}=-1.368227974\) \(a_{24}=+0.369128463\) \(a_{25}=-0.915213348\)
\(a_{26}=+1.072994783\) \(a_{27}=-0.192450090\) \(a_{28}=+0.622492637\) \(a_{29}=+1.151616376\) \(a_{30}=+0.204052699\)
\(a_{31}=-0.504974015\) \(a_{32}=-0.877005038\) \(a_{33}=+0.259409364\) \(a_{34}=-0.299890883\) \(a_{35}=-0.383002046\)
\(a_{36}=+0.157752268\) \(a_{37}=-1.733502985\) \(a_{38}=-1.826165784\) \(a_{39}=-0.510384827\) \(a_{40}=+0.186166659\)
\(a_{41}=+0.778931924\) \(a_{42}=-0.921755956\) \(a_{43}=-0.977293037\) \(a_{44}=-0.212639108\) \(a_{45}=-0.097060492\)
\(a_{46}=-1.660724885\) \(a_{47}=+0.270565811\) \(a_{48}=+0.721274916\) \(a_{49}=+0.730113933\) \(a_{50}=-1.110865741\)
\(a_{51}=+0.142647251\) \(a_{52}=+0.418364909\) \(a_{53}=-0.834359000\) \(a_{54}=-0.233591667\) \(a_{55}=+0.130830806\)
\(a_{56}=-0.840960338\) \(a_{57}=+0.868641044\) \(a_{58}=+1.397806513\) \(a_{59}=-1.590860282\) \(a_{60}=+0.079560954\)
\(a_{61}=+0.600298769\) \(a_{62}=-0.612926303\) \(a_{63}=+0.438445985\) \(a_{64}=+0.184795464\) \(a_{65}=-0.257408050\)
\(a_{66}=+0.314865354\) \(a_{67}=-1.461789457\) \(a_{68}=-0.116928641\) \(a_{69}=+0.789946789\) \(a_{70}=-0.464879422\)
\(a_{71}=+1.586140891\) \(a_{72}=-0.213116418\) \(a_{73}=+1.469310979\) \(a_{74}=-2.104087623\) \(a_{75}=+0.528398673\)
\(a_{76}=-0.712029260\) \(a_{77}=-0.590994756\) \(a_{78}=-0.619493827\) \(a_{79}=+0.531401880\) \(a_{80}=+0.363768592\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.945450360\) \(a_{83}=+1.001376503\) \(a_{84}=-0.359396292\) \(a_{85}=+0.071942873\)
\(a_{86}=-1.186216696\) \(a_{87}=-0.664886025\) \(a_{88}=+0.287266139\) \(a_{89}=-0.584886638\) \(a_{90}=-0.117809881\)
\(a_{91}=+1.162775131\) \(a_{92}=-0.647523199\) \(a_{93}=+0.291546884\) \(a_{94}=+0.328406803\) \(a_{95}=+0.438091388\)
\(a_{96}=+0.506339095\) \(a_{97}=-1.481195544\) \(a_{98}=+0.886196161\) \(a_{99}=-0.149770066\) \(a_{100}=-0.433130945\)

Showing 100 of 1228 available coefficients

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