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: \( 31.7175359147 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.172992492\) \(a_{3}=+0.577350269\) \(a_{4}=+0.375911387\) \(a_{5}=+1.357313596\)
\(a_{6}=+0.677227531\) \(a_{7}=-1.494446502\) \(a_{8}=-0.732051258\) \(a_{9}=+0.333333333\) \(a_{10}=+1.592118658\)
\(a_{11}=+0.299018697\) \(a_{12}=+0.217032540\) \(a_{13}=-0.552171348\) \(a_{14}=-1.752974527\) \(a_{15}=+0.783645370\)
\(a_{16}=-1.234602016\) \(a_{17}=-1.207537772\) \(a_{18}=+0.390997497\) \(a_{19}=+0.176931189\) \(a_{20}=+0.510229636\)
\(a_{21}=-0.862819090\) \(a_{22}=+0.350746687\) \(a_{23}=-1.845244965\) \(a_{24}=-0.422649991\) \(a_{25}=+0.842300198\)
\(a_{26}=-0.647692845\) \(a_{27}=+0.192450090\) \(a_{28}=-0.561779457\) \(a_{29}=+1.198337812\) \(a_{30}=+0.919210136\)
\(a_{31}=-0.769718664\) \(a_{32}=-0.716127638\) \(a_{33}=+0.172638525\) \(a_{34}=-1.416432740\) \(a_{35}=-2.028432556\)
\(a_{36}=+0.125303796\) \(a_{37}=-0.962219066\) \(a_{38}=+0.207538957\) \(a_{39}=-0.318796276\) \(a_{40}=-0.993623125\)
\(a_{41}=+1.723982749\) \(a_{42}=-1.012080315\) \(a_{43}=-0.092853160\) \(a_{44}=+0.112404533\) \(a_{45}=+0.452437865\)
\(a_{46}=-2.164458490\) \(a_{47}=-0.776872643\) \(a_{48}=-0.712797806\) \(a_{49}=+1.233370348\) \(a_{50}=+0.988011809\)
\(a_{51}=-0.697172258\) \(a_{52}=-0.207567497\) \(a_{53}=+0.259600122\) \(a_{54}=+0.225742510\) \(a_{55}=+0.405862143\)
\(a_{56}=+1.094011442\) \(a_{57}=+0.102151270\) \(a_{58}=+1.405641257\) \(a_{59}=-0.374387237\) \(a_{60}=+0.294581218\)
\(a_{61}=-0.788747908\) \(a_{62}=-0.902874214\) \(a_{63}=-0.498148834\) \(a_{64}=+0.394589673\) \(a_{65}=-0.749469678\)
\(a_{66}=+0.202503694\) \(a_{67}=-0.340301723\) \(a_{68}=-0.453927198\) \(a_{69}=-1.065352677\) \(a_{70}=-2.379336159\)
\(a_{71}=+0.749443709\) \(a_{72}=-0.244017086\) \(a_{73}=-1.121178180\) \(a_{74}=-1.128675741\) \(a_{75}=+0.486302246\)
\(a_{76}=+0.066510449\) \(a_{77}=-0.446867446\) \(a_{78}=-0.373945639\) \(a_{79}=-0.498073208\) \(a_{80}=-1.675742102\)
\(a_{81}=+0.111111111\) \(a_{82}=+2.022218822\) \(a_{83}=-1.062652114\) \(a_{84}=-0.324343521\) \(a_{85}=-1.639007436\)
\(a_{86}=-0.108916060\) \(a_{87}=+0.691860658\) \(a_{88}=-0.218897013\) \(a_{89}=+0.336682038\) \(a_{90}=+0.530706219\)
\(a_{91}=+0.825190539\) \(a_{92}=-0.693648594\) \(a_{93}=-0.444397278\) \(a_{94}=-0.911265778\) \(a_{95}=+0.240151109\)
\(a_{96}=-0.413456485\) \(a_{97}=-1.379973601\) \(a_{98}=+1.446734158\) \(a_{99}=+0.099672899\) \(a_{100}=+0.316630236\)

Showing 100 of 1228 available coefficients

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